西格尔零点
參考

1 2  See Iwaniec (2006).
↑  See Satz 4, §5 of Zagier (1981).
↑  χ (mod q) is even if χ(-1) = 1, and odd if χ(-1) = -1.
↑  Grönwall（英语：）, T. H. . Rendiconti di Palermo. 1913, 35: 145–159. S2CID 121161132. doi:10.1007/BF03015596 （法语）.
1 2  Landau（英语：）, E. . Göttinger Nachrichten. 1918: 285–295 （德语）.
↑  Titchmarsh（英语：）, E. C. . Rendiconti di Palermo. 1930, 54: 414–429. S2CID 119578445. doi:10.1007/BF03021203.
↑  See Chapter 16 of Davenport (1980).
↑  Landau（英语：）, E. . Acta Arithmetica（英语：）. 1936: 1–18 （德语）.
↑  Siegel, C. L.  [On the class numbers of quadratic fields]. Acta Arithmetica（英语：）. 1935, 1 (1): 83–86  [2022-11-07]. doi:10.4064/aa-1-1-83-86 . （原始内容存档于2018-03-10） （德语）.
↑  Tatuzawa, T. . Japanese Journal of Mathematics. 1951, 21: 163–178. doi:10.4099/jjm1924.21.0_163.
↑  Weinberger, P. J. . Acta Arithmetica. 1973, 22 (2): 117–124. doi:10.4064/aa-22-2-117-124.
↑  See (11) in Chapter 14 of Davenport (1980).
↑  Theorem 10.5.25 in Cohen, H. . Graduate Texts in Mathematics, Number Theory. New York: Springer-Verlag. 2007. ISBN 978-0-387-49893-5 （英语）. .
↑  Lemma 8 in Stark, H. M. . Inventiones Mathematicae. 1974-06-01, 23 (2): 135–152. ISSN 1432-1297. S2CID 119482000. doi:10.1007/BF01405166 （英语）.
1 2  Granville, A.; Stark, H.M. . Inventiones Mathematicae. 2000-03-01, 139 (3): 509–523. ISSN 1432-1297. S2CID 6901166. doi:10.1007/s002229900036 （英语）.
↑  Goldfeld, Dorian M. . Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 1976, 3 (4): 623–663  [2022-11-07]. （原始内容存档于2022-11-07） （法语）.
↑  Theorem II.4.1 in Silverman, Joseph H., , Graduate Texts in Mathematics 151, New York: Springer-Verlag, 1994, ISBN 978-0-387-94325-1 .
↑  Táfula, C. . Acta Arithmetica. 2021, 201: 1–28. S2CID 208138549. arXiv:1911.07215 . doi:10.4064/aa191118-18-5.
↑  Colmez, Pierre. . Annals of Mathematics. 1993, 138 (3): 625–683  [2022-11-07]. ISSN 0003-486X. JSTOR 2946559. doi:10.2307/2946559. （原始内容存档于2022-11-07）.
↑  Colmez, Pierre. . Compositio Mathematica. 1998-05-01, 111 (3): 359–369. ISSN 1570-5846. doi:10.1023/A:1000390105495  （英语）.
↑  See the diagram in subsection 0.6 of Colmez (1993). There is small typo in the upper right corner of this diagram, that should instead read "



−
2

h


F
a
l



(
X
)
−


1
2


log
⁡
D


{\textstyle -2h_{\mathrm {Fal} }(X)-{\frac {1}{2}}\log D}

".
↑  Proposition 2.1, Chapter X of Cornell, G.; Silverman, J. H. (编). . New York: Springer-Verlag. 1986  [2022-11-07]. ISBN 978-0-387-96311-2. （原始内容存档于2021-05-06） （英语）.
↑  Consequence of the functional equation（英语：）, where γ = 0.57721... is the Euler–Mascheroni constant（英语：）.
↑  Heath-Brown, D. R. . Proceedings of the London Mathematical Society. 1983-09-01, s3–47 (2): 193–224. ISSN 0024-6115. doi:10.1112/plms/s3-47.2.193 （英语）.
↑  . What's new. 2015-08-27  [2021-03-13]. （原始内容存档于2022-11-11） （英语）.
↑  See Chapter 9 of Nathanson, Melvyn B. . Graduate Texts in Mathematics. New York: Springer-Verlag. 1996  [2022-11-07]. ISBN 978-0-387-94656-6. （原始内容存档于2021-08-02） （英语）.
↑  Granville, A. . 2020. arXiv:2010.01211  [math.NT].
Davenport, H. . Graduate Texts in Mathematics 74. 1980  [2022-11-07]. ISBN 978-1-4757-5929-7. ISSN 0072-5285. doi:10.1007/978-1-4757-5927-3. （原始内容存档于2022-11-07） （英国英语）.
Iwaniec, H., Friedlander, J. B.; Heath-Brown, D. R.; Iwaniec, H.; Kaczorowski, J. , 编, , Analytic Number Theory: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 11–18, 2002, Lecture Notes in Mathematics 1891 (Berlin, Heidelberg: Springer), 2006, 1891: 97–132  [2021-03-13], ISBN 978-3-540-36364-4, doi:10.1007/978-3-540-36364-4_3 （英语）
Montgomery, H. L.; Vaughan, R. C. . Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press. 2006  [2022-11-07]. ISBN 978-0-521-84903-6. （原始内容存档于2022-11-07）.
Zagier, D. B. . Hochschultext. Berlin Heidelberg: Springer-Verlag. 1981. ISBN 978-3-540-10603-6 （德语）.