相关论文: Asymptotic second moment of Dirichlet $L$-function…

We compute an asymptotic formula for the mixed second moment of the $\mu$-th and $\nu$-th derivatives of quadratic Dirichlet $L$-functions over monic, irreducible polynomials in the function field setting.

Let $3\leqslant k\leqslant9$ be a fixed integer, $p$ be a prime and $d(n)$ denote the Dirichlet divisor function. We use $\Delta(x)$ to denote the error term in the asymptotic formula of the summatory function of $d(n)$. The aim of this…

We extend the work of Fouvry, Kowalski and Michel on correlation between Hecke eigenvalues of modular forms and algebraic trace functions in order to establish an asymptotic formula for a generalized cubic moment of modular L-functions at…

Given a half-integral weight holomorphic Kohnen newform $f$ on $\Gamma_0(4)$, we prove an asymptotic formula for large primes $p$ with power saving error term for \begin{equation*} \sideset{}{^*} \sum_{\chi \hspace{-0.15cm} \pmod{p}} |…

We compute the second moment in the family of quadratic Dirichlet $L$-functions with prime conductors over $\mathbb{F}_q[x]$ when the degree of the discriminant goes to infinity, obtaining one of the lower order terms. We also obtain an…

We obtain an asymptotic formula for the fourth moment of quadratic Dirichlet $L$--functions over $\mathbb{F}_q[x]$, as the base field $\mathbb{F}_q$ is fixed and the genus of the family goes to infinity. According to conjectures of Andrade…

We deal with negative square moments of Dirichlet $L$-functions. Summing over characters modulo $q$, we obtain an asymptotic formula for the negative second moment of $L(1,\chi)$ involving conductors. As an application, we give the improved…

We establish an asymptotic formula for the first moment and derive an upper bound for the second moment of L-functions associated with the complete family of primitive cubic Dirichlet characters defined over the Eisenstein field. Our…

We assume the Riemann Hypothesis and an quantitative form of the Twin Prime Conjecture, and obtain an asymptotic formula for the second moment of $S(T)$ with better error term.

We prove Motohashi's formula for a mixed second moment of the Riemann zeta function and a Dirichlet $L$-function attached to a primitive Dirichlet character modulo $q \in \mathbb{N}$. If $q$ is an odd prime, our reciprocity formula is…

We compute asymptotic formulae for the mollified first and second moments for the family of quadratic Dirichlet $L$-functions in the function field setting. As an application, we obtain non-vanishing results for the derivatives of the…

We prove an asymptotic formula for the fourth power mean of Dirichlet L-functions averaged over primitive characters to modulus q and over t\in [0,T] which is particularly effective when q \ge T. In this range the correct order of magnitude…

In this article, we derive an asymptotic formula for the second moment of $S(t)$ which includes the lower order terms using a prediction from the ratios conjecture of Conrey, Farmer and Zirnbauer. The formula matches very well with actual…

We study the fourth moment of quadratic Dirichlet $L$-functions at $s= \frac{1}{2}$. We show an asymptotic formula under the generalized Riemann hypothesis, and obtain a precise lower bound unconditionally. The proofs of these results…

In this paper we use techniques first introduced by Florea to improve the asymptotic formula for the first moment of the quadratic Dirichlet L-functions over the rational function field, running over all monic, square-free polynomials of…

Let $f$ be a Hecke cusp form for $SL(2,\mathbb{Z})$. We prove an asymptotic formula for the mixed moment of the product of $\zeta(s)$ and $L(s,f)$ on the critical line. Similarly, we prove an asymptotic formula for the mixed moment of the…

In this paper, we establish an asymptotic formula for the twisted second moments of Dirichlet $L$-functions with one and two twists when averaged over all primitive Dirichlet characters of modulus $R$, where $R$ is a monic polynomial in…

We prove a formula, with power savings, for the sixth moment of Dirichlet L-functions averaged over moduli $q$, over primitive characters $\chi$ modulo $q$, and over the critical line. Our formula agrees precisely with predictions motivated…

We give a new proof of Heath-Brown's full asymptotic expansion for the second moment of Dirichlet L-functions and we obtain a corresponding asymptotic expansion for a twisted first moment of Hecke-Maass L-functions.

Conrey, Farmer, Keating, Rubinstein, and Snaith, recently conjectured formulas for the full asymptotics of the moments of $L$-functions. In the case of the Riemann zeta function, their conjecture states that the $2k$-th absolute moment of…