article published Étienne Fouvry author Jürgen Klüners author 21202 102 department 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. Mathematical Sciences Publishers2010 eng Algebra and Number Theory 1937-065210.2140/ant.2010.4.493 45493-508 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>. É. Fouvry, J. Klüners, Algebra &#38;amp; Number Theory 4 (2010) 493–508. 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>. 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> @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} } 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> 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>. 348872022-12-23T09:10:12Z2023-03-06T10:18:14Z