The Rankin's $L$-function and Heegner points for general discriminants
نویسندگان
چکیده
منابع مشابه
Heegner points, Stark-Heegner points, and values of L-series
Elliptic curves over Q are equipped with a systematic collection of Heegner points arising from the theory of complex multiplication and defined over abelian extensions of imaginary quadratic fields. These points are the key to the most decisive progress in the last decades on the Birch and Swinnerton-Dyer conjecture: an essentially complete proof for elliptic curves over Q of analytic rank ≤ 1...
متن کاملHeegner points, Heegner cycles, and congruences
We define certain objects associated to a modular elliptic curve E and a discriminant D satisfying suitable conditions. These objects interpolate special values of the complex L-functions associated to E over the quadratic field Q( √ D), in the same way that Bernouilli numbers interpolate special values of Dirichlet L-series. Following an approach of Mazur and Tate [MT], one can make conjecture...
متن کاملHeegner Points: The Beginnings
Dick Gross and I were invited to talk about Heegner points from a historical point of view, and we agreed that I should talk first, dealing with the period before they became well known. I felt encouraged to indulge in some personal reminiscence of that period, particularly where I can support it by documentary evidence. I was fortunate enough to be working on the arithmetic of elliptic curves ...
متن کاملEquidistribution of Heegner points and the partition function
Let p(n) denote the number of partitions of a positive integer n. In this paper we study the asymptotic growth of p(n) using the equidistribution of Galois orbits of Heegner points on the modular curve X0(6). We obtain a new asymptotic formula for p(n)with an effective error termwhich is O(n−( 1 2+δ)) for some δ > 0.We then use this asymptotic formula to sharpen the classical bounds of Hardy an...
متن کاملHeegner Points and Non-vanishing of Rankin/selberg L-functions
We discuss the nonvanishing of the family of central values L( 1 2 , f ⊗ χ), where f is a fixed automorphic form on GL(2) and χ varies through class group characters of an imaginary quadratic field K = Q( √ −D), as D varies; we prove results of the nature that at least D1/5000 such twists are nonvanishing. We also discuss the related question of the rank of a fixed elliptic curve E/Q over the H...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1995
ISSN: 0386-2194
DOI: 10.3792/pjaa.71.30