Related papers: Averages of twisted L-functions

Positive twisted traces are mathematical objects that could be useful in computing certain parameters of superconformal field theories. The case when $\mathcal{A}$ is a $q$-Weyl algebra and $\rho$ is a certain antilinear automorphism of…

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…

We establish endoscopic and stable trace formulas whose discrete spectral terms are weighted by automorphic $L$-functions, by the use of basic functions that are incorporated into the global spectral and geometric coefficients. This is a…

In this paper, we prove a converse theorem for half-integral weight modular forms assuming functional equations for $L$-series with additive twists. This result is an extension of Booker, Farmer, and Lee's result in [BFL22] to the…

We introduce a twisted relative trace formula which simultaneously generalizes the twisted trace formula of Langlands et.al. (in the quadratic case) and the relative trace formula of Jacquet and Lai. Certain matching statements relating…

Under the assumption of the Riemann Hypothesis, the Linear Independence Hypothesis, and a bound on negative discrete moments of the Riemann zeta function, we prove the existence of a limiting logarithmic distribution of the normalisation of…

We develop the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular $L$-functions using multiple Dirichlet series under the generalized Riemann…

We extend to Dirichlet L-functions associated with arbitrary primitive characters a range of objects and properties -- including Eisenstein series and period functions -- that were originally introduced and studied by Lewis and Zagier…

We prove mixed-norm estimates for circular averages with respect to $\alpha$-dimensional fractal measures on $\mathbb{R}^2$, using circle tangency bounds when $\alpha \in (0,1]$ and a $\delta$-discretized slicing lemma for fractals when…

We prove a generalization to the totally real field case of the Waldspurger's formula relating the Fourier coefficient of a half integral weight form and the central value of the L-function of an integral weight form. Our proof is based on…

We define "splitting functions of level l" for any integer l>0. These functions generalize Dwork's splitting functions : they allow us to represent additive characters of order $p^l$. Then we use these functions to obtain a Stickleberger…

In this paper, over imaginary quadratic fields, we consider the family of $L$-functions $L (s, f)$ for an orthonormal basis of spherical Hecke--Maass forms $f$ with Archimedean parameter $t_f$. We establish asymptotic formulae for the…

Let f be a classical holomorphic cusp form for SL_2(Z) of weight k which is a normalized eigenfunction for the Hecke algebra, and let \lambda(n) be its eigenvalues. In this paper we study "shifted convolution sums" of the eigenvalues…

In this note, we give a detailed proof of an asymptotic for averages of coefficients of a class of degree three $L$-functions which can be factorized as a product of a degree one and a degree two $L$-functions. We emphasize that we can…

Let $f$ and $g$ be two holomorphic or Hecke-Maass primitive cusp forms for $SL(2,\mathbb{Z})$ and $\chi$ be a primitive Dirichlet character of modulus $p$, an odd prime. A subconvex bound for the central values of the Rankin-Selberg…

We formulate an explicit refinement of B\"ocherer's conjecture for Siegel modular forms of degree 2 and squarefree level, relating weighted averages of Fourier coefficients with special values of L-functions. To achieve this, we compute the…

Fix $g$ a self-dual Hecke-Maass form for $SL_3(\mathbb{Z})$. Let $f$ be a holomorphic newform of prime level $q$ and fixed weight. Conditional on a lower bound for a short sum of squares of Fourier coefficients of $f$, we prove a…

We prove an asymptotic formula for the second moment of automorphic L-functions of even weight and prime power level. The error term is estimated uniformly in all parameters: level, weight, shift and twist.

This paper is devoted to a weighted version of the one-level density of the non-trivial zeros of $L$-functions, tilted by a power of the $L$-function evaluated at the central point. Assuming the Riemann Hypothesis and the ratio conjecture,…

We estimate the mean square of a short exponential sum involving Fourier coefficients of a cusp form with a linear twist, a smooth weight function, and a relatively short averaging interval.