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Conference Paper

The Fourier coefficients of Eisenstein series newforms


Thompson,  Lola
Max Planck Institute for Mathematics, Max Planck Society;

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Linowitz, B., & Thompson, L. (2019). The Fourier coefficients of Eisenstein series newforms. In Automorphic forms and related topics (pp. 169-176). Providence, RI: American Mathematical Society.

Cite as: https://hdl.handle.net/21.11116/0000-0004-69B4-B
In this article, we study the Fourier coefficients of Eisenstein series newforms. We obtain a sharp refinement of the strong multiplicity-one theorem by showing that the density of primes p for which the pth Hecke eigenvalues of two distinct Eisenstein series newforms differ is of the form 1/n for some n ≥ 2. Additionally, we show that if f is an Eisenstein series newform whose Fourier coefficients af (n) are real then there is a constant δ > 0 such that the
sequence (af (n))n≤x has at least δx sign changes.