Mean values with cubic characters

Abstract

We investigate various mean value problems involving order three primitive Dirichlet characters. In particular, we obtain an asymptotic formula for the first moment of central values of the Dirichlet L-functions associated to this family, with a power saving in the error term. We also obtain a large-sieve type result for order three (and six) Dirichlet characters.

22 pages; greatly shortened, simplified and corrected version

References in corpus (3)

• The first moment of quadratic Dirichlet L-functions
• Vanishing and Non-Vanishing Dirichlet Twists of L-Functions of Elliptic Curves
• On the Low-lying zeros of Hasse-Weil L-functions for Elliptic Curves

Cited by in corpus (26)

• The first moment of quadratic Dirichlet L-functions
• The third moment of quadratic Dirichlet L-functions
• On the Low-lying zeros of Hasse-Weil L-functions for Elliptic Curves
• One level density of low-lying zeros of families of $L$-functions
• The mean values of cubic L-functions over function fields
• Moments of Quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields
• Central values of derivatives of Dirichlet L-functions
• Moments of central values of quartic Dirichlet $L$-functions
• The Distribution of p-Torsion in Degree p Cyclic Fields
• Large values of $L(1,\chi )$ for $k$-th order characters $\chi$ and applications to character sums
• First Moment of Hecke $L$-functions with quartic characters at the central point
• Non-vanishing for cubic $L$--functions
• Mean values of cubic and quartic Dirichlet Characters
• Zero-Density Theorems for Families of Dirichlet $L$-functions
• One-level density and non-vanishing for cubic $L$-functions over the Eisenstein field
• Bounds for moments of cubic and quartic Dirichlet $L$-functions
• Mean values of some Hecke characters
• On Primes Represented by Cubic Polynomials
• Bias in cubic Gauss sums: Patterson's conjecture
• First Moments of Some Hecke $L$-functions of Prime Moduli
• Primes $p\equiv 1\mathrm{mod}d$ and $a^{(p-1)/d}\equiv 1\mathrm{mod}p$}
• On abelian cubic fields with large class number
• Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(\omega )$
• Moments of central values of cubic Hecke $L$-functions of $\mathbb{Q}(i)$
• First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters
• Weighted first moments of some special quadratic Dirichlet $L$-functions