Related papers: The fourth moment of Dirichlet L-functions

We evaluate the twisted four moment on the critical line of the family of Dirichlet $L$-functions to a fixed prime power modulus, obtaining an asymptotic formula with a power saving error term.

For a positive integer $q\not\equiv 2 \pmod 4$, this work considers the fourth moment of Dirichlet $L$-functions averaged over both $t\in [0,T]$ and primitive characters to modulus $q$. An asymptotic formula with a power saving from both…

We study the moments of the Dirichlet L-function when defined over the polynomial ring over finite fields. We find an asymptotic formula to the fourth moment of the central value of Dirichlet L functions in this context. We also find a…

The asymptotic formula of the fourth moment of Dirichlet $L$-functions at the central value was predicted in a conjecture by J. B. Conrey, D. W. Farmer, J. P. Keating, M. O. Rubinstein, and N. C. Snaith, and the prime moduli case was proved…

We prove an asymptotic formula with a power saving error term for the fourth moment of the family of Dirichlet $L$-functions to modulus $q$ mollified by a Dirichlet polynomial of length $q^{\frac1{22}-\ve}$, valid for all moduli…

We evaluate some twisted fourth moment of Dirichlet $L$-functions at the central point s=1/2 and for prime moduli q. The principal tool is a careful analysis of a shifted convolution problem involving the divisor function using spectral…

We prove an asymptotic formula for the second moment of a product of two Dirichlet L-functions on the critical line, which has a power saving in the error term and which is uniform with respect to the involved Dirichlet characters. As…

We study the third moment of quadratic Dirichlet L-functions, obtaining an error term of size $O(X^{3/4 + \varepsilon})$.

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…

We study the first moment of primitive quadratic Dirichlet $L$-functions. Assuming the Riemann hypothesis and the generalized Lindel\"of hypothesis, we obtain an asymptotic formula at the central point with error $O(X^{1/4+\epsilon})$, and…

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…

Extending a result of Heath-Brown, we establish an asymptotic formula for the fourth moment of central values of Dirichlet $L$-functions attached to primitive characters $\pmod q$.

In this paper, we study moments of the central values of quartic Dirichlet $L$-functions and establish quantitative non-vanishing result for these $L$-values.

In this paper, we study the $k$-th moment of central values of the family of quadratic Dirichlet $L$-functions of moduli $8p$, with $p$ ranging over odd primes. Assuming the truth of the generlized Riemann hypothesis, we establish sharp…

We evaluate the first moment of central values of the family of quadratic Dirichlet $L$-functions using the method of double Dirichlet series. Under the generalized Riemann hypothesis, we prove an asymptotic formula with an error term of…

We prove results on moments of $L$-functions in the function field setting, where the moment averages are taken over primitive characters of modulus $R$, where $R$ is a polynomial in $\mathbb{F}_q [T]$. We consider the behaviour as…

We obtain an asymptotic formula for the smoothly weighted first moment of primitive quadratic Dirichlet L-functions at the central point, with an error term that is "square-root" of the main term. Our approach uses a recursive technique…

A new reciprocity formula for Dirichlet $L$-functions associated to an arbitrary primitive Dirichlet character of prime modulus $q$ is established. We find an identity relating the fourth moment of individual Dirichlet $L$-functions in the…

In this article, we study the second moment of cubic Dirichlet L-functions at the central point $s=1/2$ over the rational function field $\mathbb{F}_q(T)$, where $q$ is a power of an odd prime satisfying $q \equiv 2 \pmod{3}$. Our result…

There has recently been some interest in optimizing the error term in the asymptotic for the fourth moment of Dirichlet L-functions and a closely related mixed moment of L-functions involving automorphic L-functions twisted by Dirichlet…