Heegner zeros of theta functions

Jimenez-Urroz, Jorge; Yang, Tonghai

doi:10.1090/S0002-9947-03-03277-X

Heegner zeros of theta functions
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by Jorge Jimenez-Urroz and Tonghai Yang PDF

Trans. Amer. Math. Soc. 355 (2003), 4137-4149 Request permission

Abstract:

Heegner divisors play an important role in number theory. However, little is known on whether a modular form has Heegner zeros. In this paper, we start to study this question for a family of classical theta functions, and prove a quantitative result, which roughly says that many of these theta functions have a Heegner zero of discriminant $-7$. This leads to some interesting questions on the arithmetic of certain elliptic curves, which we also address here.

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