Weighted first moments of some special quadratic Dirichlet LL-functions

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 $s=1/2$.Comment: 7 page

First Moment of Hecke LL-functions with quartic characters at the central point

In this paper, we study the first moment of central values of Hecke $L$-functions associated with quartic characters.Comment: 11 page

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

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.Comment: 25 pages. arXiv admin note: text overlap with arXiv:0910.506