Weighted first moments of some special quadratic Dirichlet $L$-functions

Abstract

In this paper, we obtain asymptotic formulas for weighted first moments of central values of families of primitive quadratic Dirichlet $L$-functions whose conductors comprise only primes that split in a given quadratic number field. We then deduce a non-vanishing result of these $L$-functions at the point $s=1/2$.

7 pages

References in corpus (3)

• The subconvexity problem for $\GL_{2}$
• Mean values with cubic characters
• The first moment of quadratic Dirichlet L-functions