arXiv subjects
Publications and source records attributed to C. C. Corrigan.
In this article, we establish a large sieve inequality for additive characters to moduli in the range of appropriate integer polynomials of degree two. As an application, we derive a weighted zero-density estimate for twists of $L$-functions associated to multiplicative characters with conductor of this form.
The main purpose of this paper is to establish bounds on the second moment of $L\big(\tfrac{1}{2}+it,χ\big)$, averaged over families of fixed order characters. A discrete version of the main result is also stated, from which zero-density estimates pertaining to fixed order characters are derived.
In this paper, we use the Weyl-bound for Dirichlet $L$-functions to derive zero-density estimates for $L$-functions associated to families of fixed-order Dirichlet characters. The results improve on previous bounds given by the author when $\sigma$ is sufficiently distanced from the critical line.
In this paper, we prove some zero density theorems for certain families of Dirichlet $L$-functions. More specifically, the subjects of our interest are the collections of Dirichlet $L$-functions associated with characters to moduli from certain sparse sets and of certain fixed orders.