Related papers: The fourth moment of Dirichlet L-functions

We establish upper bounds for shifted moments of cubic and quartic Dirichlet $L$-functions under the generalized Riemann hypothesis. As an application, we prove bounds for moments of cubic and quartic Dirichlet character sums.

We establish lower bounds for the $2k$-th moment of families of quadratic Dirichlet $L$-functions at the central point for all real $k<0$, assuming a conjecture of S. Chowla on the non-vanishing of these $L$-values.

We evaluate the twisted first moment of central values of the family of primitive quadratic Dirichlet $L$-functions using the method of double Dirichlet series together with a recursive argument. Our main result is an asymptotic formula…

We prove an asymptotic formula for the eighth moment of Dirichlet $L$-functions averaged over primitive characters $\chi$ modulo $q$, over all moduli $q\leq Q$ and with a short average on the critical line. Previously the same result was…

We establish sharp upper bounds for shifted moments of quadratic Dirichlet $L$-function under the generalized Riemann hypothesis. Our result is then used to prove bounds for moments of quadratic Dirichlet character sums.

We establish unconditional sharp upper bounds of the $k$-th moments of the family of quadratic Dirichlet $L$-functions at the central point for $0 \leq k \leq 2$.

We compute the first and second moment of the spinor L-function at the central point of Siegel modular forms of large weight k with power saving error term and give applications to non-vanishing.

We evaluate the twisted first moment of central values of the product of a quadratic Dirichlet $L$-function and a quadratic twist of a modular $L$-function.

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

We compute the asymptotics of the fourth moment of the Riemann zeta function times an arbitrary Dirichlet polynomial of length $T^{{1/11} - \epsilon}$

The moments of central values of families of L-functions have recently attracted much attention and, with the work of Keating and Snaith, there are now precise conjectures for their limiting values. We develop a simple method to establish…

We investigate the mean value of the first moment of primitive quartic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum \begin{equation*} \sum_{\substack{\chi\ primitive\ quartic\\ \chi^2…

We establish sharp upper bounds on shifted moments of quadratic Dirichlet $L$-functions over function fields. As an application, we prove some bounds for moments of quadratic Dirichlet character sums over function fields.

In this paper, we establish the expected order of magnitude of the $k$th-moment of quadratic Dirichlet $L$-functions associated to hyperelliptic curves of genus $g$ as well as of prime moduli over a fixed finite field $\mathbb{F}_{q}$ for…

In this paper, we establish sharp upper bounds on shifted moments of the family of Dirichlet $L$-functions to a fixed modulus over function fields. We apply the result to obtain upper bounds on moments of Dirichlet character sums over…

We study the 2k-th power moment of Dirichlet L-functions L(s,\chi) at the centre of the critical strip (s=1/2), where the average is over all primitive characters \chi (mod q). We extend to this case the hybrid Euler-Hadamard product…

We establish an asymptotic formula with a power-saving error term for the twisted mixed moment of Dirichlet $L$-functions and automorphic $L$-functions twisted by all primitive characters modulo $q$, valid for all admissible moduli. As a…

We prove the q-aspect analogue of Heath-Brown's result on the twelfth power moment of the Riemann zeta function for Dirichlet L-functions to odd prime power moduli. Our results rely on the p-adic method of stationary phase for sums of…

We obtain the asymptotic main term of moments of arbitrary derivatives of $L$-functions in the function field setting. Specifically, the first, second, and mixed fourth moments. The average is taken over all non-trivial characters of a…

We verify the conjecture of [CFKRS] for the mean square near the critical point of Dirichlet L-functions for a composite modulus q. We also prove a kind of reciprocity formula when the second moment for a prime modulus is twisted by a…