Uniform bounds for Fourier coefficients of theta-series with arithmetic applications
Non-vanishing of class group -functions at the central point
Let be an imaginary quadratic field, and denote by its class number. It is shown that there is an absolute constant such that for sufficiently large at least of the distinct -functions do not vanish at the central point .
On the 4-norm of an automorphic form
We prove the optimal upper bound where runs over an orthonormal basis of Maass cusp forms of prime level and bounded spectral parameter.
Kloosterman sums in residue classes
We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any fixed primitive congruence class up to bounds towards the Ramanujan conjecture.
On the number of integers represented by systems of Abelian norm forms
Bounds for modular L-functions in the level aspect
Bounding hyperbolic and spherical coefficients of Maass forms
We develop a new method to bound the hyperbolic and spherical Fourier coefficients of Maass forms defined with respect to arbitrary uniform lattices.
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