[{"_id":"41993","department":[{"_id":"314"}],"user_id":"237","keyword":["Electrochemistry","Spectroscopy","Surfaces and Interfaces","Condensed Matter Physics","General Materials Science"],"language":[{"iso":"eng"}],"publication":"Langmuir","type":"journal_article","status":"public","publisher":"American Chemical Society (ACS)","date_updated":"2023-02-10T14:38:57Z","volume":26,"author":[{"first_name":"Frank M.","full_name":"Bayer, Frank M.","last_name":"Bayer"},{"last_name":"Hiltrop","full_name":"Hiltrop, Karl","first_name":"Karl"},{"last_name":"Huber","full_name":"Huber, Klaus","id":"237","first_name":"Klaus"}],"date_created":"2023-02-10T14:37:27Z","title":"Hydrogen-Bond-Induced Heteroassembly in Binary Colloidal Systems","doi":"10.1021/la101831x","publication_identifier":{"issn":["0743-7463","1520-5827"]},"publication_status":"published","issue":"17","year":"2010","intvolume":"        26","page":"13815-13822","citation":{"ieee":"F. M. Bayer, K. Hiltrop, and K. Huber, “Hydrogen-Bond-Induced Heteroassembly in Binary Colloidal Systems,” <i>Langmuir</i>, vol. 26, no. 17, pp. 13815–13822, 2010, doi: <a href=\"https://doi.org/10.1021/la101831x\">10.1021/la101831x</a>.","chicago":"Bayer, Frank M., Karl Hiltrop, and Klaus Huber. “Hydrogen-Bond-Induced Heteroassembly in Binary Colloidal Systems.” <i>Langmuir</i> 26, no. 17 (2010): 13815–22. <a href=\"https://doi.org/10.1021/la101831x\">https://doi.org/10.1021/la101831x</a>.","ama":"Bayer FM, Hiltrop K, Huber K. Hydrogen-Bond-Induced Heteroassembly in Binary Colloidal Systems. <i>Langmuir</i>. 2010;26(17):13815-13822. doi:<a href=\"https://doi.org/10.1021/la101831x\">10.1021/la101831x</a>","apa":"Bayer, F. M., Hiltrop, K., &#38; Huber, K. (2010). Hydrogen-Bond-Induced Heteroassembly in Binary Colloidal Systems. <i>Langmuir</i>, <i>26</i>(17), 13815–13822. <a href=\"https://doi.org/10.1021/la101831x\">https://doi.org/10.1021/la101831x</a>","bibtex":"@article{Bayer_Hiltrop_Huber_2010, title={Hydrogen-Bond-Induced Heteroassembly in Binary Colloidal Systems}, volume={26}, DOI={<a href=\"https://doi.org/10.1021/la101831x\">10.1021/la101831x</a>}, number={17}, journal={Langmuir}, publisher={American Chemical Society (ACS)}, author={Bayer, Frank M. and Hiltrop, Karl and Huber, Klaus}, year={2010}, pages={13815–13822} }","mla":"Bayer, Frank M., et al. “Hydrogen-Bond-Induced Heteroassembly in Binary Colloidal Systems.” <i>Langmuir</i>, vol. 26, no. 17, American Chemical Society (ACS), 2010, pp. 13815–22, doi:<a href=\"https://doi.org/10.1021/la101831x\">10.1021/la101831x</a>.","short":"F.M. Bayer, K. Hiltrop, K. Huber, Langmuir 26 (2010) 13815–13822."}},{"year":"2010","page":"3027-3035","intvolume":"        43","citation":{"apa":"Lages, S., Michels, R., &#38; Huber, K. (2010). Coil-Collapse and Coil-Aggregation due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution. <i>Macromolecules</i>, <i>43</i>(6), 3027–3035. <a href=\"https://doi.org/10.1021/ma9027239\">https://doi.org/10.1021/ma9027239</a>","short":"S. Lages, R. Michels, K. Huber, Macromolecules 43 (2010) 3027–3035.","bibtex":"@article{Lages_Michels_Huber_2010, title={Coil-Collapse and Coil-Aggregation due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution}, volume={43}, DOI={<a href=\"https://doi.org/10.1021/ma9027239\">10.1021/ma9027239</a>}, number={6}, journal={Macromolecules}, publisher={American Chemical Society (ACS)}, author={Lages, S. and Michels, R. and Huber, Klaus}, year={2010}, pages={3027–3035} }","mla":"Lages, S., et al. “Coil-Collapse and Coil-Aggregation Due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution.” <i>Macromolecules</i>, vol. 43, no. 6, American Chemical Society (ACS), 2010, pp. 3027–35, doi:<a href=\"https://doi.org/10.1021/ma9027239\">10.1021/ma9027239</a>.","chicago":"Lages, S., R. Michels, and Klaus Huber. “Coil-Collapse and Coil-Aggregation Due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution.” <i>Macromolecules</i> 43, no. 6 (2010): 3027–35. <a href=\"https://doi.org/10.1021/ma9027239\">https://doi.org/10.1021/ma9027239</a>.","ieee":"S. Lages, R. Michels, and K. Huber, “Coil-Collapse and Coil-Aggregation due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution,” <i>Macromolecules</i>, vol. 43, no. 6, pp. 3027–3035, 2010, doi: <a href=\"https://doi.org/10.1021/ma9027239\">10.1021/ma9027239</a>.","ama":"Lages S, Michels R, Huber K. Coil-Collapse and Coil-Aggregation due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution. <i>Macromolecules</i>. 2010;43(6):3027-3035. doi:<a href=\"https://doi.org/10.1021/ma9027239\">10.1021/ma9027239</a>"},"publication_identifier":{"issn":["0024-9297","1520-5835"]},"publication_status":"published","issue":"6","title":"Coil-Collapse and Coil-Aggregation due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution","doi":"10.1021/ma9027239","publisher":"American Chemical Society (ACS)","date_updated":"2023-02-10T14:39:59Z","volume":43,"author":[{"first_name":"S.","full_name":"Lages, S.","last_name":"Lages"},{"full_name":"Michels, R.","last_name":"Michels","first_name":"R."},{"first_name":"Klaus","last_name":"Huber","full_name":"Huber, Klaus","id":"237"}],"date_created":"2023-02-10T14:39:34Z","status":"public","publication":"Macromolecules","type":"journal_article","keyword":["Materials Chemistry","Inorganic Chemistry","Polymers and Plastics","Organic Chemistry"],"language":[{"iso":"eng"}],"_id":"41995","department":[{"_id":"314"}],"user_id":"237"},{"date_created":"2023-02-13T08:19:11Z","author":[{"full_name":" Richter, D","last_name":" Richter","first_name":"D"},{"full_name":"Hafenbrak, R","last_name":"Hafenbrak","first_name":"R"},{"first_name":"Klaus D.","id":"85353","full_name":"Jöns, Klaus D.","last_name":"Jöns"},{"last_name":"Schulz","full_name":"Schulz, W-M","first_name":"W-M"},{"first_name":"M","full_name":"Eichfelder, M","last_name":"Eichfelder"},{"last_name":"Heldmaier","full_name":"Heldmaier, M","first_name":"M"},{"first_name":"R","full_name":"Roßbach, R","last_name":"Roßbach"},{"first_name":"M","full_name":"Jetter, M","last_name":"Jetter"},{"first_name":"P","full_name":"Michler, P","last_name":"Michler"}],"volume":21,"date_updated":"2023-02-13T08:44:48Z","title":"Low-density MOVPE grown InGaAs QDs exhibiting ultra-narrow single exciton linewidths","citation":{"chicago":"Richter, D, R Hafenbrak, Klaus D. Jöns, W-M Schulz, M Eichfelder, M Heldmaier, R Roßbach, M Jetter, and P Michler. “Low-Density MOVPE Grown InGaAs QDs Exhibiting Ultra-Narrow Single Exciton Linewidths.” Nanotechnology , 2010.","ieee":"D.  Richter <i>et al.</i>, “Low-density MOVPE grown InGaAs QDs exhibiting ultra-narrow single exciton linewidths,” vol. 21. 2010.","ama":"Richter D, Hafenbrak R, Jöns KD, et al. Low-density MOVPE grown InGaAs QDs exhibiting ultra-narrow single exciton linewidths. 2010;21.","apa":"Richter, D., Hafenbrak, R., Jöns, K. D., Schulz, W.-M., Eichfelder, M., Heldmaier, M., Roßbach, R., Jetter, M., &#38; Michler, P. (2010). <i>Low-density MOVPE grown InGaAs QDs exhibiting ultra-narrow single exciton linewidths</i> (No. 125606; Vol. 21).","mla":"Richter, D., et al. <i>Low-Density MOVPE Grown InGaAs QDs Exhibiting Ultra-Narrow Single Exciton Linewidths</i>. 125606, 2010.","short":"D.  Richter, R. Hafenbrak, K.D. Jöns, W.-M. Schulz, M. Eichfelder, M. Heldmaier, R. Roßbach, M. Jetter, P. Michler, 21 (2010).","bibtex":"@article{ Richter_Hafenbrak_Jöns_Schulz_Eichfelder_Heldmaier_Roßbach_Jetter_Michler_2010, series={Nanotechnology }, title={Low-density MOVPE grown InGaAs QDs exhibiting ultra-narrow single exciton linewidths}, volume={21}, number={125606}, author={ Richter, D and Hafenbrak, R and Jöns, Klaus D. and Schulz, W-M and Eichfelder, M and Heldmaier, M and Roßbach, R and Jetter, M and Michler, P}, year={2010}, collection={Nanotechnology } }"},"intvolume":"        21","year":"2010","series_title":"Nanotechnology ","user_id":"71124","department":[{"_id":"623"}],"_id":"42030","language":[{"iso":"eng"}],"article_number":"125606 ","type":"conference","status":"public"},{"title":"The Internet – serving the revolution?","date_created":"2023-02-28T01:40:52Z","author":[{"full_name":"Fuchs, Christian","id":"21863","last_name":"Fuchs","orcid":"0000-0003-0589-4579","first_name":"Christian"}],"date_updated":"2023-02-28T01:42:03Z","citation":{"apa":"Fuchs, C. (2010). The Internet – serving the revolution? <i>Counterfire</i>.","mla":"Fuchs, Christian. “The Internet – Serving the Revolution?” <i>Counterfire</i>, 2010.","short":"C. Fuchs, Counterfire (2010).","bibtex":"@article{Fuchs_2010, title={The Internet – serving the revolution?}, journal={Counterfire}, author={Fuchs, Christian}, year={2010} }","ama":"Fuchs C. The Internet – serving the revolution? <i>Counterfire</i>. 2010.","ieee":"C. Fuchs, “The Internet – serving the revolution?,” <i>Counterfire</i>, 2010.","chicago":"Fuchs, Christian. “The Internet – Serving the Revolution?” <i>Counterfire</i>, 2010."},"year":"2010","language":[{"iso":"eng"}],"extern":"1","user_id":"49063","department":[{"_id":"136"}],"publication_date":"2010-04-24","_id":"42613","status":"public","type":"newspaper_article","publication":"Counterfire"},{"article_type":"original","extern":"1","_id":"8179","department":[{"_id":"623"},{"_id":"7"}],"user_id":"71541","status":"public","type":"journal_article","main_file_link":[{"url":"https://arxiv.org/abs/0810.4507","open_access":"1"}],"date_updated":"2023-02-28T11:04:38Z","oa":"1","volume":10,"author":[{"first_name":"Sevag","orcid":"0000-0002-9992-3379","last_name":"Gharibian","id":"71541","full_name":"Gharibian, Sevag"}],"intvolume":"        10","page":"343-360","citation":{"chicago":"Gharibian, Sevag. “Strong NP-Hardness of the Quantum Separability Problem.” <i>Quantum Information &#38; Computation</i> 10, no. 3{\\ &#38; }4 (2010): 343–60.","ieee":"S. Gharibian, “Strong NP-hardness of the quantum separability problem,” <i>Quantum Information &#38; Computation</i>, vol. 10, no. 3{\\ &#38; }4, pp. 343–360, 2010.","ama":"Gharibian S. Strong NP-hardness of the quantum separability problem. <i>Quantum Information &#38; Computation</i>. 2010;10(3{\\ &#38; }4):343-360.","bibtex":"@article{Gharibian_2010, title={Strong NP-hardness of the quantum separability problem}, volume={10}, number={3{\\ &#38; }4}, journal={Quantum Information &#38; Computation}, author={Gharibian, Sevag}, year={2010}, pages={343–360} }","mla":"Gharibian, Sevag. “Strong NP-Hardness of the Quantum Separability Problem.” <i>Quantum Information &#38; Computation</i>, vol. 10, no. 3{\\ &#38; }4, 2010, pp. 343–60.","short":"S. Gharibian, Quantum Information &#38; Computation 10 (2010) 343–360.","apa":"Gharibian, S. (2010). Strong NP-hardness of the quantum separability problem. <i>Quantum Information &#38; Computation</i>, <i>10</i>(3{\\ &#38; }4), 343–360."},"publication_status":"published","language":[{"iso":"eng"}],"external_id":{"arxiv":["0810.4507"]},"abstract":[{"text":"Given the density matrix rho of a bipartite quantum state, the quantum separability problem asks whether rho is entangled or separable. In 2003, Gurvits showed that this problem is NP-hard if rho is located within an inverse exponential (with respect to dimension) distance from the border of the set of separable quantum states. In this paper, we extend this NP-hardness to an inverse polynomial distance from the separable set. The result follows from a simple combination of works by Gurvits, Ioannou, and Liu. We apply our result to show (1) an immediate lower bound on the maximum distance between a bound entangled state and the separable set (assuming P != NP), and (2) NP-hardness for the problem of determining whether a completely positive trace-preserving linear map is entanglement-breaking.","lang":"eng"}],"publication":"Quantum Information & Computation","title":"Strong NP-hardness of the quantum separability problem","date_created":"2019-03-01T12:09:59Z","year":"2010","issue":"3{\\&}4"},{"keyword":["Statistics","Probability and Uncertainty","Mathematics (miscellaneous)"],"language":[{"iso":"eng"}],"publication":"Annals of Mathematics","abstract":[{"lang":"eng","text":"We give asymptotic upper and lower bounds for the number of squarefree d (0 < d ≤ X) such that the equation x² − dy²= −1 is solvable. These estimates, as usual, can equivalently be interpreted in terms of real quadratic fields with a fundamental unit with norm −1 and give strong evidence in the direction of a conjecture due to P. Stevenhagen."}],"publisher":"Annals of Mathematics","date_created":"2022-12-23T09:09:02Z","title":"On the negative Pell equation","issue":"3","year":"2010","_id":"34886","department":[{"_id":"102"}],"user_id":"93826","type":"journal_article","status":"public","date_updated":"2023-03-06T09:50:37Z","volume":172,"author":[{"last_name":"Fouvry","full_name":"Fouvry, Étienne","first_name":"Étienne"},{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"}],"doi":"10.4007/annals.2010.172.2035","publication_identifier":{"issn":["0003-486X"]},"publication_status":"published","page":"2035-2104","intvolume":"       172","citation":{"apa":"Fouvry, É., &#38; Klüners, J. (2010). On the negative Pell equation. <i>Annals of Mathematics</i>, <i>172</i>(3), 2035–2104. <a href=\"https://doi.org/10.4007/annals.2010.172.2035\">https://doi.org/10.4007/annals.2010.172.2035</a>","short":"É. Fouvry, J. Klüners, Annals of Mathematics 172 (2010) 2035–2104.","bibtex":"@article{Fouvry_Klüners_2010, title={On the negative Pell equation}, volume={172}, DOI={<a href=\"https://doi.org/10.4007/annals.2010.172.2035\">10.4007/annals.2010.172.2035</a>}, number={3}, journal={Annals of Mathematics}, publisher={Annals of Mathematics}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={2035–2104} }","mla":"Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.” <i>Annals of Mathematics</i>, vol. 172, no. 3, Annals of Mathematics, 2010, pp. 2035–104, doi:<a href=\"https://doi.org/10.4007/annals.2010.172.2035\">10.4007/annals.2010.172.2035</a>.","chicago":"Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.” <i>Annals of Mathematics</i> 172, no. 3 (2010): 2035–2104. <a href=\"https://doi.org/10.4007/annals.2010.172.2035\">https://doi.org/10.4007/annals.2010.172.2035</a>.","ieee":"É. Fouvry and J. Klüners, “On the negative Pell equation,” <i>Annals of Mathematics</i>, vol. 172, no. 3, pp. 2035–2104, 2010, doi: <a href=\"https://doi.org/10.4007/annals.2010.172.2035\">10.4007/annals.2010.172.2035</a>.","ama":"Fouvry É, Klüners J. On the negative Pell equation. <i>Annals of Mathematics</i>. 2010;172(3):2035-2104. doi:<a href=\"https://doi.org/10.4007/annals.2010.172.2035\">10.4007/annals.2010.172.2035</a>"}},{"_id":"34888","user_id":"93826","department":[{"_id":"102"}],"status":"public","type":"journal_article","doi":"10.1112/plms/pdp057","date_updated":"2023-03-06T10:16:54Z","author":[{"full_name":"Fouvry, Étienne","last_name":"Fouvry","first_name":"Étienne"},{"last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202","first_name":"Jürgen"}],"volume":101,"citation":{"apa":"Fouvry, É., &#38; Klüners, J. (2010). The parity of the period of the continued fraction of d. <i>Proceedings of the London Mathematical Society</i>, <i>101</i>(2), 337–391. <a href=\"https://doi.org/10.1112/plms/pdp057\">https://doi.org/10.1112/plms/pdp057</a>","bibtex":"@article{Fouvry_Klüners_2010, title={The parity of the period of the continued fraction of d}, volume={101}, DOI={<a href=\"https://doi.org/10.1112/plms/pdp057\">10.1112/plms/pdp057</a>}, number={2}, journal={Proceedings of the London Mathematical Society}, publisher={Wiley}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={337–391} }","short":"É. Fouvry, J. Klüners, Proceedings of the London Mathematical Society 101 (2010) 337–391.","mla":"Fouvry, Étienne, and Jürgen Klüners. “The Parity of the Period of the Continued Fraction of d.” <i>Proceedings of the London Mathematical Society</i>, vol. 101, no. 2, Wiley, 2010, pp. 337–91, doi:<a href=\"https://doi.org/10.1112/plms/pdp057\">10.1112/plms/pdp057</a>.","chicago":"Fouvry, Étienne, and Jürgen Klüners. “The Parity of the Period of the Continued Fraction of d.” <i>Proceedings of the London Mathematical Society</i> 101, no. 2 (2010): 337–91. <a href=\"https://doi.org/10.1112/plms/pdp057\">https://doi.org/10.1112/plms/pdp057</a>.","ieee":"É. Fouvry and J. Klüners, “The parity of the period of the continued fraction of d,” <i>Proceedings of the London Mathematical Society</i>, vol. 101, no. 2, pp. 337–391, 2010, doi: <a href=\"https://doi.org/10.1112/plms/pdp057\">10.1112/plms/pdp057</a>.","ama":"Fouvry É, Klüners J. The parity of the period of the continued fraction of d. <i>Proceedings of the London Mathematical Society</i>. 2010;101(2):337-391. doi:<a href=\"https://doi.org/10.1112/plms/pdp057\">10.1112/plms/pdp057</a>"},"intvolume":"       101","page":"337-391","publication_status":"published","publication_identifier":{"issn":["0024-6115"]},"related_material":{"link":[{"relation":"confirmation","url":"https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=fc7ab412993fd2bf0069de42fbef1ecc69137755"}]},"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We call a positive square-free integer d special, if d is not divisible by primes congruent to 3 mod 4. We show that the period of the expansion of in continued fractions is asymptotically more often odd than even, when we restrict to special integers. We note that this period is always even for a non-special square-free integer d. It is well known that the above period is odd if and only if the negative Pell equation x²−dy²=−1 is solvable. The latter problem is solvable if and only if the narrow and the ordinary class groups of ℚ(√d) are equal. In a prior work we fully described the asymptotics of the 4-ranks of those class groups. Here we get the first non-trivial results about the asymptotic behavior of the 8-rank of the narrow class group. For example, we show that more than 76% of the quadratic fields ℚ(√d), where d is special, have the property that the 8-rank of the narrow class group is zero."}],"publication":"Proceedings of the London Mathematical Society","title":"The parity of the period of the continued fraction of d","publisher":"Wiley","date_created":"2022-12-23T09:22:49Z","year":"2010","issue":"2"},{"title":"On the Spiegelungssatz for the 4-rank","doi":"10.2140/ant.2010.4.493","publisher":"Mathematical Sciences Publishers","date_updated":"2023-03-06T10:18:14Z","author":[{"first_name":"Étienne","full_name":"Fouvry, Étienne","last_name":"Fouvry"},{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"date_created":"2022-12-23T09:10:12Z","volume":4,"year":"2010","citation":{"mla":"Fouvry, Étienne, and Jürgen Klüners. “On the Spiegelungssatz for the 4-Rank.” <i>Algebra &#38;amp; Number Theory</i>, vol. 4, no. 5, Mathematical Sciences Publishers, 2010, pp. 493–508, doi:<a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>.","short":"É. Fouvry, J. Klüners, Algebra &#38;amp; Number Theory 4 (2010) 493–508.","bibtex":"@article{Fouvry_Klüners_2010, title={On the Spiegelungssatz for the 4-rank}, volume={4}, DOI={<a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>}, number={5}, journal={Algebra &#38;amp; Number Theory}, publisher={Mathematical Sciences Publishers}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={493–508} }","apa":"Fouvry, É., &#38; Klüners, J. (2010). On the Spiegelungssatz for the 4-rank. <i>Algebra &#38;amp; Number Theory</i>, <i>4</i>(5), 493–508. <a href=\"https://doi.org/10.2140/ant.2010.4.493\">https://doi.org/10.2140/ant.2010.4.493</a>","ama":"Fouvry É, Klüners J. On the Spiegelungssatz for the 4-rank. <i>Algebra &#38;amp; Number Theory</i>. 2010;4(5):493-508. doi:<a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>","ieee":"É. Fouvry and J. Klüners, “On the Spiegelungssatz for the 4-rank,” <i>Algebra &#38;amp; Number Theory</i>, vol. 4, no. 5, pp. 493–508, 2010, doi: <a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>.","chicago":"Fouvry, Étienne, and Jürgen Klüners. “On the Spiegelungssatz for the 4-Rank.” <i>Algebra &#38;amp; Number Theory</i> 4, no. 5 (2010): 493–508. <a href=\"https://doi.org/10.2140/ant.2010.4.493\">https://doi.org/10.2140/ant.2010.4.493</a>."},"page":"493-508","intvolume":"         4","publication_status":"published","publication_identifier":{"issn":["1937-0652"]},"issue":"5","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"_id":"34887","user_id":"93826","department":[{"_id":"102"}],"abstract":[{"text":"Let d be a nonsquare positive integer. We give the value of the natural probability that the narrow ideal class groups of the quadratic fields ℚ(√d) and ℚ(√−d) have the same 4-ranks. 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