标题： 条件性下界关于中心值的分布：模形式的情况 显示英文标题

标题： Conditional lower bounds on the distribution of central values: the case of modular forms

摘要： Radziwill和Soundararajan揭示了低级零点与$L$-函数中心值之间的联系，他们在椭圆曲线二次扭曲的情况下进行了实例化。 本文研究了水平方面模形式族的情况，并证明了相关L函数中心值的对数大致按照正态分布，均值为-(1/2)log log c(f)，方差为log log c(f)，其中c(f)是f的解析导数，这符合Keating-Snaith猜想的预测。 显示英文摘要

摘要： Radziwill and Soundararajan unveiled a connection between low-lying zeros and central values of $L$-functions, which they instantiated in the case of quadratic twists of an elliptic curve. This paper addresses the case of the family of modular forms in the level aspect, and proves that the logarithms of central values of associated L-functions approximately distribute along a normal law with mean -(1/2)log log c(f) and variance log log c(f), where c(f) is the analytic conductor of f, as predicted by the Keating-Snaith conjecture.