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arXiv · 1703.08473

Additive bases with coefficients of newforms

Victor Cuauhtemoc Garcia·Florin Nicolae
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Abstract

Let $f(z)=\sum_{n=1}^{\infty}a(n) e^{2\pi i nz}$ be a normalized Hecke eigenform in $S_{2k}^{\text{new}}(\Gamma_0(N))$ with integer Fourier coefficients. We prove that there exists a constant $C(f)>0$ such that any integer is a sum of at most $C(f)$ coefficients $a(n) $. It holds $C(f)\ll_{\varepsilon,k}N^{\frac{6k-3}{16}+\varepsilon}$.

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Victor Cuauhtemoc Garcia, Florin Nicolae. 2017-03-24. Additive bases with coefficients of newforms. https://arxiv.org/abs/1703.08473

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