Biases in Moments of the Dirichlet Coefficients in One-Parameter Families of Elliptic Curves
Steven J. Miller,
Yan Weng
Abstract:Elliptic curves arise in many important areas of modern number theory. One way to study them is to take local data, the number of solutions modulo a prime p, and create an L-function. The behavior of this global object is related to two of the seven Clay Millenial Problems: the Birch and Swinnerton-Dyer Conjecture and the Generalized Riemann Hypothesis. We study one-parameter families over Q(T). We look at the r-th moment of the series expansion of the L-function (the p-th coefficient is related to the number … Show more
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