The additive divisor problem and its analogs for Fourier coefficients of cusp forms. I.
The analytic order of III for modular elliptic curves
In this note we extend the computations described in [4] by computing the analytic order of the Tate-Shafarevich group III for all the curves in each isogeny class ; in [4] we considered the strong Weil curve only. While no new methods are involved here, the results have some interesting features suggesting ways in which strong Weil curves may be distinguished from other curves in their isogeny class.
The construction of modular forms as products of transforms of the Dedekind eta function
The distribution of the eigenvalues of Hecke operators
The Doi-Naganuma Lifting of Quaternary Theta Series.
The Eisenstein family for the modular group along closed geodescis.
The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, II
The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, I
The Fourth Moment of Ramanujan ..-Function.
The L2-Lefschetz numbers of Hecke operators.
The l-adic representations attached to a certain noncongruence subgroup.
The level 1 weight 2 case of Serre's conjecture.
The L-function L3(s, ...) is entire.
The Logarithm of the Dedekind n-Function.
The logarithm of the Siegel function
The Maaß-Space on the Half-Space of Quaternions of Degree 2.
The modular degree and the congruence number of a weight 2 cusp form
The period function of the nonholomorphic Eisenstein series for .
The second moment of quadratic twists of modular L-functions
We study the second moment of the central values of quadratic twists of a modular -function. Unconditionally, we obtain a lower bound which matches the conjectured asymptotic formula, while on GRH we prove the asymptotic formula itself.
The shifted fourth moment of automorphic L-functions of prime power level
We prove an asymptotic formula for the fourth moment of automorphic L-functions of level , where p is a fixed prime number and ν → ∞. This is a continuation of work by Rouymi, who computed the asymptotics of the first three moments at a prime power level, and a generalization of results obtained for a prime level by Duke, Friedlander Iwaniec and Kowalski, Michel VanderKam.