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Gross, who presented an elliptic curve test for Mersenneprimes Mₚ=2ᵖ−1, we propose a similar test with elliptic curves for generalizedThabit primesK(h, n) := h·2ⁿ−1 for any positive odd number h and any integer n> log₂(h)+2."}],"type":"book_chapter","publication":"Integers","language":[{"iso":"eng"}],"extern":"1","user_id":"93826","department":[{"_id":"102"}],"_id":"42805"},{"author":[{"full_name":"Lorch, David","last_name":"Lorch","first_name":"David"},{"last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus","first_name":"Markus"}],"volume":16,"date_updated":"2023-04-04T07:57:04Z","doi":"10.1112/s1461157013000107","publication_status":"published","publication_identifier":{"issn":["1461-1570"]},"citation":{"ieee":"D. Lorch and M. Kirschmer, “Single-class genera of positive integral lattices,” <i>LMS Journal of Computation and Mathematics</i>, vol. 16, pp. 172–186, 2013, doi: <a href=\"https://doi.org/10.1112/s1461157013000107\">10.1112/s1461157013000107</a>.","chicago":"Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” <i>LMS Journal of Computation and Mathematics</i> 16 (2013): 172–86. <a href=\"https://doi.org/10.1112/s1461157013000107\">https://doi.org/10.1112/s1461157013000107</a>.","ama":"Lorch D, Kirschmer M. Single-class genera of positive integral lattices. <i>LMS Journal of Computation and Mathematics</i>. 2013;16:172-186. doi:<a href=\"https://doi.org/10.1112/s1461157013000107\">10.1112/s1461157013000107</a>","apa":"Lorch, D., &#38; Kirschmer, M. (2013). Single-class genera of positive integral lattices. <i>LMS Journal of Computation and Mathematics</i>, <i>16</i>, 172–186. <a href=\"https://doi.org/10.1112/s1461157013000107\">https://doi.org/10.1112/s1461157013000107</a>","mla":"Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” <i>LMS Journal of Computation and Mathematics</i>, vol. 16, Wiley, 2013, pp. 172–86, doi:<a href=\"https://doi.org/10.1112/s1461157013000107\">10.1112/s1461157013000107</a>.","bibtex":"@article{Lorch_Kirschmer_2013, title={Single-class genera of positive integral lattices}, volume={16}, DOI={<a href=\"https://doi.org/10.1112/s1461157013000107\">10.1112/s1461157013000107</a>}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Lorch, David and Kirschmer, Markus}, year={2013}, pages={172–186} }","short":"D. Lorch, M. Kirschmer, LMS Journal of Computation and Mathematics 16 (2013) 172–186."},"page":"172-186","intvolume":"        16","user_id":"93826","department":[{"_id":"102"}],"_id":"42796","extern":"1","type":"journal_article","status":"public","date_created":"2023-03-07T08:34:28Z","publisher":"Wiley","title":"Single-class genera of positive integral lattices","year":"2013","language":[{"iso":"eng"}],"keyword":["Computational Theory and Mathematics","General Mathematics"],"publication":"LMS Journal of Computation and Mathematics","abstract":[{"lang":"eng","text":"We give an enumeration of all positive definite primitive Z-lattices in dimension n ≥ 3 whose genus consists of a single isometry class. This is achieved by using bounds obtained from the Smith–Minkowski–Siegel mass formula to computationally construct the square-free determinant lattices with this property, and then repeatedly calculating pre-images under a mapping first introduced by G. L. Watson.\r\n\r\nWe hereby complete the classification of single-class genera in dimensions 4 and 5 and correct some mistakes in Watson’s classifications in other dimensions. A list of all single-class primitive Z-lattices has been compiled and incorporated into the Catalogue of Lattices."}]},{"citation":{"chicago":"Baier, Robert, and Mirko Hessel-von Molo. “Newton’s Method and Secant Method for Set-Valued Mappings.” In <i>Large-Scale Scientific Computing</i>. Berlin, Heidelberg, 2012. <a href=\"https://doi.org/10.1007/978-3-642-29843-1_9\">https://doi.org/10.1007/978-3-642-29843-1_9</a>.","ieee":"R. Baier and M. H. Molo, “Newton’s Method and Secant Method for Set-Valued Mappings,” in <i>Large-Scale Scientific Computing</i>, Berlin, Heidelberg, 2012.","ama":"Baier R, Molo MH. Newton’s Method and Secant Method for Set-Valued Mappings. In: <i>Large-Scale Scientific Computing</i>. 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Berlin, Heidelberg. <a href=\"https://doi.org/10.1007/978-3-642-29843-1_9\">https://doi.org/10.1007/978-3-642-29843-1_9</a>"},"place":"Berlin, Heidelberg","year":"2012","publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["9783642298424","9783642298431"]},"publication_status":"published","doi":"10.1007/978-3-642-29843-1_9","title":"Newton’s Method and Secant Method for Set-Valued Mappings","author":[{"full_name":"Baier, Robert","last_name":"Baier","first_name":"Robert"},{"first_name":"Mirko Hessel-von","full_name":"Molo, Mirko Hessel-von","last_name":"Molo"}],"date_created":"2020-04-15T07:59:49Z","date_updated":"2022-01-06T06:52:52Z","status":"public","publication":"Large-Scale Scientific Computing","type":"book_chapter","department":[{"_id":"101"}],"user_id":"15701","_id":"16516"},{"publication_status":"published","publication_identifier":{"issn":["1612-3956"],"isbn":["9783642250996","9783642251009"]},"citation":{"apa":"Dellnitz, M., Dignath, F., Flaßkamp, K., Molo, M. H., Krüger, M., Timmermann, R., &#38; Zheng, Q. (2012). Modelling and Analysis of the Nonlinear Dynamics of the Transrapid and Its Guideway. In <i>Mathematics in Industry</i>. Berlin, Heidelberg. <a href=\"https://doi.org/10.1007/978-3-642-25100-9_14\">https://doi.org/10.1007/978-3-642-25100-9_14</a>","short":"M. Dellnitz, F. Dignath, K. Flaßkamp, M.H. Molo, M. Krüger, R. Timmermann, Q. Zheng, in: Mathematics in Industry, Berlin, Heidelberg, 2012.","mla":"Dellnitz, Michael, et al. “Modelling and Analysis of the Nonlinear Dynamics of the Transrapid and Its Guideway.” <i>Mathematics in Industry</i>, 2012, doi:<a href=\"https://doi.org/10.1007/978-3-642-25100-9_14\">10.1007/978-3-642-25100-9_14</a>.","bibtex":"@inbook{Dellnitz_Dignath_Flaßkamp_Molo_Krüger_Timmermann_Zheng_2012, place={Berlin, Heidelberg}, title={Modelling and Analysis of the Nonlinear Dynamics of the Transrapid and Its Guideway}, DOI={<a href=\"https://doi.org/10.1007/978-3-642-25100-9_14\">10.1007/978-3-642-25100-9_14</a>}, booktitle={Mathematics in Industry}, author={Dellnitz, Michael and Dignath, Florian and Flaßkamp, Kathrin and Molo, Mirko Hessel-von and Krüger, Martin and Timmermann, Robert and Zheng, Qinghua}, year={2012} }","chicago":"Dellnitz, Michael, Florian Dignath, Kathrin Flaßkamp, Mirko Hessel-von Molo, Martin Krüger, Robert Timmermann, and Qinghua Zheng. “Modelling and Analysis of the Nonlinear Dynamics of the Transrapid and Its Guideway.” In <i>Mathematics in Industry</i>. Berlin, Heidelberg, 2012. <a href=\"https://doi.org/10.1007/978-3-642-25100-9_14\">https://doi.org/10.1007/978-3-642-25100-9_14</a>.","ieee":"M. Dellnitz <i>et al.</i>, “Modelling and Analysis of the Nonlinear Dynamics of the Transrapid and Its Guideway,” in <i>Mathematics in Industry</i>, Berlin, Heidelberg, 2012.","ama":"Dellnitz M, Dignath F, Flaßkamp K, et al. Modelling and Analysis of the Nonlinear Dynamics of the Transrapid and Its Guideway. In: <i>Mathematics in Industry</i>. Berlin, Heidelberg; 2012. doi:<a href=\"https://doi.org/10.1007/978-3-642-25100-9_14\">10.1007/978-3-642-25100-9_14</a>"},"place":"Berlin, Heidelberg","year":"2012","author":[{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"},{"first_name":"Florian","last_name":"Dignath","full_name":"Dignath, Florian"},{"last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin","first_name":"Kathrin"},{"last_name":"Molo","full_name":"Molo, Mirko Hessel-von","first_name":"Mirko Hessel-von"},{"full_name":"Krüger, Martin","last_name":"Krüger","first_name":"Martin"},{"full_name":"Timmermann, Robert","last_name":"Timmermann","first_name":"Robert"},{"first_name":"Qinghua","full_name":"Zheng, Qinghua","last_name":"Zheng"}],"date_created":"2020-04-16T05:08:17Z","date_updated":"2022-01-06T06:52:52Z","doi":"10.1007/978-3-642-25100-9_14","title":"Modelling and Analysis of the Nonlinear Dynamics of the Transrapid and Its Guideway","type":"book_chapter","publication":"Mathematics in Industry","status":"public","user_id":"15701","department":[{"_id":"101"}],"_id":"16576"}]