Nonvanishing of quadratic Dirichlet L-functions at s=1/2

Abstract

We show that for a positive proportion of fundamental discriminants d, L(1/2,chi_d) != 0. Here chi_d is the primitive quadratic Dirichlet character of conductor d.

42 pages, published version

Cited by in corpus (20)

• A Symplectic Test of the L-Functions Ratios Conjecture
• The Mean Value of $L(\frac{1}{2},\chi )$ in the Hyperelliptic Ensemble
• Real zeros of quadratic Dirichlet L-functions
• The first moment of quadratic Dirichlet L-functions
• The third moment of quadratic Dirichlet L-functions
• On the reciprocity law for the twisted second moment of Dirichlet $L$-functions
• An Orthogonal Test of the $L$-functions Ratios Conjecture, II
• The mean values of cubic L-functions over function fields
• One level density of low-lying zeros of families of $L$-functions
• Moments of central values of quartic Dirichlet $L$-functions
• Non-vanishing of Dirichlet L-functions in Galois orbits
• Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli
• On the nonvanishing of elliptic curve L-functions at the central point
• A note on Dedekind zeta values at 1/2
• One level density of low-lying zeros of quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields
• One-level density of quadratic twists of $L$-functions
• First Moments of Some Hecke $L$-functions of Prime Moduli
• First moment of central values of quadratic Dirichlet $L$-functions
• Moments and non-vanishing of $L$-functions over thin subgroups
• Moments and One level density of certain unitary families of Hecke {$L$}-functions