arXiv subjects

Fabian Waibel

Publications and source records attributed to Fabian Waibel.

3 recordsLinked to original sources

arXiv2021

Uniform bounds for norms of theta series and arithmetic applications

We prove uniform bounds for the Petersson norm of the cuspidal part of the theta series. This gives an improved asymptotic formula for the number of representations by a quadratic form. As an application, we show that every integer $n \neq 0,4,7 \,(\operatorname{mod}8)$ is represented as $n= x_1^2 + x_2^2 + x_3^3$ for integers $x_1,x_2,x_3$ such that the product $x_1x_2x_3$ has at most 72 prime divisors.

math.NT↗

arXiv2019

Moments of Spinor L-Functions and symplectic Kloosterman sums

We compute the second moment of spinor $L$-functions at central points of Siegel modular forms on congruence subgroups of large prime level $N$ and give applications to non-vanishing.

math.NT↗

arXiv2017

Fourier coefficients of half-integral weight cusp forms and Waring's problem

Extending the approach of Iwaniec and Duke, we present strong uniform bounds for Fourier coefficients of half-integral weight cusp forms of level $N$. As an application, we consider a Waring-type problem with sums of mixed powers.

math.NT↗