Siegel zero (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Siegel zero" in English language version.

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11doi.org

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5semanticscholar.org

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2harvard.edu

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arxiv.org

Táfula, C. (2021). "On Landau–Siegel zeros and heights of singular moduli". Acta Arithmetica. 201: 1–28. arXiv:1911.07215. doi:10.4064/aa191118-18-5. S2CID 208138549.
Granville, A. (2020). "Sieving intervals and Siegel zeros". arXiv:2010.01211 [math.NT].

doi.org

Grönwall, T. H. (1913). "Sur les séries de Dirichlet correspondant à des charactères complexes". Rendiconti di Palermo (in French). 35: 145–159. doi:10.1007/BF03015596. S2CID 121161132.
Titchmarsh, E. C. (1930). "A divisor problem". Rendiconti di Palermo. 54: 414–429. doi:10.1007/BF03021203. S2CID 119578445.
Siegel, C. L. (1935). "Über die Klassenzahl quadratischer Zahlkörper" [On the class numbers of quadratic fields]. Acta Arithmetica (in German). 1 (1): 83–86. doi:10.4064/aa-1-1-83-86.
Tatuzawa, T. (1951). "On a theorem of Siegel". Japanese Journal of Mathematics. 21: 163–178. doi:10.4099/jjm1924.21.0_163.
Weinberger, P. J. (1973). "Exponents of the class group of complex quadratic fields". Acta Arithmetica. 22 (2): 117–124. doi:10.4064/aa-22-2-117-124.
Lemma 8 in Stark, H. M. (1974-06-01). "Some effective cases of the Brauer-Siegel Theorem". Inventiones Mathematicae. 23 (2): 135–152. Bibcode:1974InMat..23..135S. doi:10.1007/BF01405166. ISSN 1432-1297. S2CID 119482000.
Granville, A.; Stark, H.M. (2000-03-01). "ABC implies no "Siegel zeros" for L-functions of characters with negative discriminant". Inventiones Mathematicae. 139 (3): 509–523. Bibcode:2000InMat.139..509G. doi:10.1007/s002229900036. ISSN 1432-1297. S2CID 6901166.
Táfula, C. (2021). "On Landau–Siegel zeros and heights of singular moduli". Acta Arithmetica. 201: 1–28. arXiv:1911.07215. doi:10.4064/aa191118-18-5. S2CID 208138549.
Colmez, Pierre (1993). "Periodes des Variétés Abéliennes à Multiplication Complexe". Annals of Mathematics. 138 (3): 625–683. doi:10.2307/2946559. ISSN 0003-486X. JSTOR 2946559.
Colmez, Pierre (1998-05-01). "Sur la hauteur de Faltings des variétés abéliennes à multiplication complexe". Compositio Mathematica. 111 (3): 359–369. doi:10.1023/A:1000390105495 (inactive 9 January 2025). ISSN 1570-5846.{{cite journal}}: CS1 maint: DOI inactive as of January 2025 (link)
Heath-Brown, D. R. (1983-09-01). "Prime Twins and Siegel Zeros". Proceedings of the London Mathematical Society. s3-47 (2): 193–224. doi:10.1112/plms/s3-47.2.193. ISSN 0024-6115.

harvard.edu

ui.adsabs.harvard.edu

Lemma 8 in Stark, H. M. (1974-06-01). "Some effective cases of the Brauer-Siegel Theorem". Inventiones Mathematicae. 23 (2): 135–152. Bibcode:1974InMat..23..135S. doi:10.1007/BF01405166. ISSN 1432-1297. S2CID 119482000.
Granville, A.; Stark, H.M. (2000-03-01). "ABC implies no "Siegel zeros" for L-functions of characters with negative discriminant". Inventiones Mathematicae. 139 (3): 509–523. Bibcode:2000InMat.139..509G. doi:10.1007/s002229900036. ISSN 1432-1297. S2CID 6901166.

icm.edu.pl

pldml.icm.edu.pl

Siegel, C. L. (1935). "Über die Klassenzahl quadratischer Zahlkörper" [On the class numbers of quadratic fields]. Acta Arithmetica (in German). 1 (1): 83–86. doi:10.4064/aa-1-1-83-86.

jstor.org

Colmez, Pierre (1993). "Periodes des Variétés Abéliennes à Multiplication Complexe". Annals of Mathematics. 138 (3): 625–683. doi:10.2307/2946559. ISSN 0003-486X. JSTOR 2946559.

numdam.org

Goldfeld, Dorian M. (1976). "The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer". Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (in French). 3 (4): 623–663.

oup.com

academic.oup.com

Heath-Brown, D. R. (1983-09-01). "Prime Twins and Siegel Zeros". Proceedings of the London Mathematical Society. s3-47 (2): 193–224. doi:10.1112/plms/s3-47.2.193. ISSN 0024-6115.

semanticscholar.org

api.semanticscholar.org

Grönwall, T. H. (1913). "Sur les séries de Dirichlet correspondant à des charactères complexes". Rendiconti di Palermo (in French). 35: 145–159. doi:10.1007/BF03015596. S2CID 121161132.
Titchmarsh, E. C. (1930). "A divisor problem". Rendiconti di Palermo. 54: 414–429. doi:10.1007/BF03021203. S2CID 119578445.
Lemma 8 in Stark, H. M. (1974-06-01). "Some effective cases of the Brauer-Siegel Theorem". Inventiones Mathematicae. 23 (2): 135–152. Bibcode:1974InMat..23..135S. doi:10.1007/BF01405166. ISSN 1432-1297. S2CID 119482000.
Granville, A.; Stark, H.M. (2000-03-01). "ABC implies no "Siegel zeros" for L-functions of characters with negative discriminant". Inventiones Mathematicae. 139 (3): 509–523. Bibcode:2000InMat.139..509G. doi:10.1007/s002229900036. ISSN 1432-1297. S2CID 6901166.
Táfula, C. (2021). "On Landau–Siegel zeros and heights of singular moduli". Acta Arithmetica. 201: 1–28. arXiv:1911.07215. doi:10.4064/aa191118-18-5. S2CID 208138549.

springer.com

Theorem 10.5.25 in Cohen, H. (2007). Number Theory: Volume II: Analytic and Modern Tools. Graduate Texts in Mathematics, Number Theory. New York: Springer-Verlag. ISBN 978-0-387-49893-5..
Proposition 2.1, Chapter X of Cornell, G.; Silverman, J. H., eds. (1986). Arithmetic Geometry. New York: Springer-Verlag. ISBN 978-0-387-96311-2.
See Chapter 9 of Nathanson, Melvyn B. (1996). Additive Number Theory The Classical Bases. Graduate Texts in Mathematics. New York: Springer-Verlag. ISBN 978-0-387-94656-6.

terrytao.wordpress.com

"Heath-Brown's theorem on prime twins and Siegel zeroes". What's new. 2015-08-27. Retrieved 2021-03-13.

uqam.ca

labmath.uqam.ca

Kani, Ernst (2011). "Idoneal numbers and some generalizations" (PDF). Annales des Sciences Mathématiques du Québec. 35 (2). Remark 24.

worldcat.org

search.worldcat.org

Lemma 8 in Stark, H. M. (1974-06-01). "Some effective cases of the Brauer-Siegel Theorem". Inventiones Mathematicae. 23 (2): 135–152. Bibcode:1974InMat..23..135S. doi:10.1007/BF01405166. ISSN 1432-1297. S2CID 119482000.
Granville, A.; Stark, H.M. (2000-03-01). "ABC implies no "Siegel zeros" for L-functions of characters with negative discriminant". Inventiones Mathematicae. 139 (3): 509–523. Bibcode:2000InMat.139..509G. doi:10.1007/s002229900036. ISSN 1432-1297. S2CID 6901166.
Colmez, Pierre (1993). "Periodes des Variétés Abéliennes à Multiplication Complexe". Annals of Mathematics. 138 (3): 625–683. doi:10.2307/2946559. ISSN 0003-486X. JSTOR 2946559.
Colmez, Pierre (1998-05-01). "Sur la hauteur de Faltings des variétés abéliennes à multiplication complexe". Compositio Mathematica. 111 (3): 359–369. doi:10.1023/A:1000390105495 (inactive 9 January 2025). ISSN 1570-5846.{{cite journal}}: CS1 maint: DOI inactive as of January 2025 (link)
Heath-Brown, D. R. (1983-09-01). "Prime Twins and Siegel Zeros". Proceedings of the London Mathematical Society. s3-47 (2): 193–224. doi:10.1112/plms/s3-47.2.193. ISSN 0024-6115.