Related papers: One-level density estimates for Dirichlet L-functi…

Let $\mathbb{K} = \mathbb{Q}(\sqrt{-d})$ be an imaginary quadratic number field of class number $1$ and $\mathcal{O}_{\mathbb{K}}$ its ring of integers. We study a family of Hecke $L$-functions associated to angular characters on the…

Let K be a number field containing the n-th roots of unity for some n > 2. We prove a uniform subconvexity result for a family of double Dirichlet series built out of central values of Hecke L-functions of n-th order characters of K. The…

In this paper, we estimate the proportion of zeros of Dirichlet $L$-functions on the critical line. Using Feng's mollifier and an asymptotic formula for the mean square of Dirichlet $L$-functions, we prove that averaged over primitive…

The Generalized Riemann Hypothesis implies that at least 50% of the central values $L \left( \frac{1}{2},\chi\right)$ are non-vanishing as $\chi$ ranges over primitive characters modulo $q$. We show that one may unconditionally go beyond…

We show, for any $q\ge 3$ and distinct reduced residues $a,b \pmod q$, the existence of certain hypothetical sets of zeros of Dirichlet $L$-functions lying off the critical line implies that $\pi(x;q,a)<\pi(x;q,b)$ for a set of real $x$ of…

We introduce an infinite family of approximations for a Dirichlet $L$-function $L(s, \chi)$ arising from truncated Euler products. These approximations are entire functions and satisfy the same functional equation as $L(s, \chi)$. We…

We study the nonvanishing of twists of automorphic L-functions at the centre of the critical strip. Given a primitive character \chi modulo D satisfying some technical conditions, we prove that the twisted L-functions L(f.\chi,s) do not…

Let C(q,+) be the set of even, primitive Dirichlet characters (mod q). Using the mollifier method we show that L^{(k)}(1/2,chi) is not equal to zero for almost all the characters chi in C(q,+) when k and q are large. Here, L^{(k)}(s,chi) is…

Let $L(s,\chi)$ be the Dirichlet $L$-function associated to a non-principal primitive Dirichlet character $\chi$ defined modulo $q$, where $q\ge 3$. We prove, under the assumption of the Generalised Riemann Hypothesis, the validity of…

Let $f$ be a Hecke-Maass cusp form for the full modular group and let $\chi$ be a primitive Dirichlet character modulo a prime $q$. Let $s_0=\sigma_0+it_0$ with $\frac{1}{2}\leq\sigma_0<1$. We improve the error term for the first moment of…

Let $q$ be a prime, $\chi$ be a non-principal Dirichlet character $\bmod\ q$ and $L(s,\chi)$ be the associated Dirichlet $L$-function. For every odd prime $q\le 10^7$, we show that $L(1,\chi_\square) > c_{1} \log q$ and $\beta < 1-…

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…

Let $F$ be a linear combination of $N\geq 1$ Dirichlet $L$-functions attached to even (or odd) primitive characters with the same modulus. Selberg proved that a positive proportion of non-trivial zeros of $F$ lie on the critical line. Our…

In this paper, we prove the simultaneous non-vanishing of four Dirichlet $L$-functions at any point on the critical line. More precisely, let $\chi_1,\ldots,\chi_4$ be even Dirichlet characters modulo $D_1,\ldots, D_4$ respectively, where…

We calculate murmuration densities for two families of Dirichlet characters. The first family contains complex Dirichlet characters normalized by their Gauss sums. Integrating the first density over a geometric interval yields a murmuration…

We prove that more than nine percent of the central values $L(\frac{1}{2},\chi_p)$ are non-zero, where $p\equiv 1 \pmod{8}$ ranges over primes and $\chi_p$ is the real primitive Dirichlet character of conductor $p$. Previously, it was not…

In a recent work arXiv:2004.14450, it has been shown that $L$-functions associated with arbitrary non-zero cusp forms take large values at the central critical point. The goal of this note is to derive analogous results for twists of…

In this paper, we prove that if the Fourier coefficients of a $\mathrm{SL}(3,\mathbb{Z})$ Hecke--Maa\ss\ cusp form $\pi$ are not too correlated with additive characters, then there exists infinitely many Dirichlet characters such that…

Under the generalized Riemann hypothesis, we use Beurling-Selberg extremal functions to bound the mean and mean square of the argument of Dirichlet $L$-functions to a large prime modulus $q$. As applications, we give alternative proofs of…

We study the conjecture that $\sum_{n\leq x} \chi(n)=o(x)$ for any primitive Dirichlet character $\chi \pmod q$ with $x\geq q^\epsilon$, which is known to be true if the Riemann Hypothesis holds for $L(s,\chi)$. We show that it holds under…