Large Sieve Inequalities for Special Characters to Prime Square Moduli

In this paper, we develop a large sieve type inequality for some special characters whose moduli are squares of primes. Our result gives non-trivial estimate in certain ranges.Comment: six page

An Improvement of a Large Sieve Inequality in High Dimensions

In this paper, we present an improvement of a large sieve type inequality in high dimensions and discuss its implications on a related problem.Comment: 7 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

Moments of central values of cubic Hecke LL-functions of Q(i)\mathbb{Q}(i)

In this paper, we study moments of central values of cubic Hecke $L$-functions in $\mathbb{Q}(i)$, and establish quantitative non-vanishing result for those values.Comment: 15 page

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

On Primes Represented by Quadratic Polynomials

This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.Comment: six(6) pages, minor changes were mad

On Primes Represented by Cubic Polynomials

In this paper, we prove a theorem on the distribution of primes in cubic progressions on average.Comment: 14 pages, to appear in Math.