Moments of symmetric square L-functions on GL(3)
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929347145760768 |
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| author | Blomer, Valentin Comtat, Félicien |
| author_facet | Blomer, Valentin Comtat, Félicien |
| contents | We give an asymptotic formula with power saving error term for the twisted first moment of symmetric square L-functions on GL(3) in the level aspect. As applications, we obtain non-vanishing results as well as lower bounds of the expected order of magnitude for all even moments, supporting the random matrix model for a unitary ensemble. Besides the GL(3) Kuznetsov formula, the ingredients include detailed local computations at ramified places, including root numbers and orthonormalization of oldforms and Eisenstein series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10827 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moments of symmetric square L-functions on GL(3) Blomer, Valentin Comtat, Félicien Number Theory We give an asymptotic formula with power saving error term for the twisted first moment of symmetric square L-functions on GL(3) in the level aspect. As applications, we obtain non-vanishing results as well as lower bounds of the expected order of magnitude for all even moments, supporting the random matrix model for a unitary ensemble. Besides the GL(3) Kuznetsov formula, the ingredients include detailed local computations at ramified places, including root numbers and orthonormalization of oldforms and Eisenstein series. |
| title | Moments of symmetric square L-functions on GL(3) |
| topic | Number Theory |
| url | https://arxiv.org/abs/2405.10827 |