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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 that feeds the result back into itself, successively improving the error term.
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 follow closely a
We obtain the asymptotic formula with an error term $O(X^{frac{1}{2} + varepsilon})$ for the smoothed first moment of quadratic twists of modular $L$-functions. We also give a similar result for the smoothed first moment of the first derivative of qu
We prove an asymptotic formula for the twisted first moment of Maass form symmetric square L-functions on the critical line and at the critical point. The error term is estimated uniformly with respect to all parameters.
Let $qge3$ be an integer, $chi$ be a Dirichlet character modulo $q$, and $L(s,chi)$ denote the Dirichlet $L$-functions corresponding to $chi$. In this paper, we show some special function series, and give some new identities for the Dirichlet $L$-fun
We look at the values of two Dirichlet $L$-functions at the Riemann zeros (or a horizontal shift of them). Off the critical line we show that for a positive proportion of these points the pairs of values of the two $L$-functions are linearly independ