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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 quadratic twists of modular $L$-functions. The argument is largely based on Youngs recursive method [19,20].
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
We prove an asymptotic formula with a power saving error term for the (pure or mixed) second moment of central values of L-functions of any two (possibly equal) fixed cusp forms f, g twisted by all primitive characters modulo q, valid for all suffici
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 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.
We calculate certain wide moments of central values of Rankin--Selberg $L$-functions $L(piotimes Omega, 1/2)$ where $pi$ is a cuspidal automorphic representation of $mathrm{GL}_2$ over $mathbb{Q}$ and $Omega$ is a Hecke character (of conductor $1$) o