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arXiv · 2603.15197

Variance of GL(2) Fourier coefficients in arithmetic progressions

Laurent Montaigu
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Abstract

We improve a result of Lau and Zhao on the variance of Fourier coefficients of primitive cuspidal modular forms for SL2(Z) in arithmetic progressions. This is achieved by using bounds on the first moment of Rankin-Selberg L-functions in the height aspect and non-trivial estimates for shifted convolution sums.

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Laurent Montaigu. 2026-03-16. Variance of GL(2) Fourier coefficients in arithmetic progressions. https://arxiv.org/abs/2603.15197

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