Variance of GL(2) Fourier coefficients in arithmetic progressions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914586675904512 |
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| author | Montaigu, Laurent |
| author_facet | Montaigu, Laurent |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15197 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Variance of GL(2) Fourier coefficients in arithmetic progressions Montaigu, Laurent Number Theory 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. |
| title | Variance of GL(2) Fourier coefficients in arithmetic progressions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.15197 |