One level density of low-lying zeros of quadratic and quartic Hecke $L$-functions

Abstract

In this paper, we prove some one level density results for the low-lying zeros of famliies of quadratic and quartic Hecke $L$-functions of the Gaussian field. As corollaries, we deduce that, respectively, at least $94.27\%$ and $5\%$ of the members of the quadratic family and the quartic family do not vanish at the central point.

25 pages. arXiv admin note: text overlap with arXiv:0910.5063

References in corpus (1)

• On the Low-lying zeros of Hasse-Weil L-functions for Elliptic Curves

Cited by in corpus (12)

• Moments and Non-vanishing of central values of Quadratic Hecke $L$-functions in the Gaussian Field
• The fourth moment of central values of quadratic Hecke $L$-functions in the Gaussian field
• One-level density of quadratic twists of $L$-functions
• One level density of low-lying zeros of quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields
• Mean values of some Hecke characters
• First Moments of Some Hecke $L$-functions of Prime Moduli
• Average values of quadratic Hecke character sums
• Non-vanishing of central values of quadratic Hecke $L$-functions of prime moduli in the Gaussian field
• Moments of central values of cubic Hecke $L$-functions of $\mathbb{Q}(i)$
• Moments and One level density of certain unitary families of Hecke {$L$}-functions
• Real zeros of quadratic Hecke $L$-functions
• One level density of low-lying zeros of quadratic Hecke $L$-functions to prime moduli