Approximations of $SL(3,\mathbb{Z})$ Hecke-Maass $L$-Functions by short Dirichlet polynomials
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917207952326656 |
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| author | Kim, Jiseong |
| author_facet | Kim, Jiseong |
| contents | We study averages of $L$-functions associated with Hecke-Maass cusp forms for $SL(3,\mathbb{Z})$, multiplied by Dirichlet polynomials built from the Fourier coefficients of the cusp forms. To prove this, we employ a variant of the Kuznetsov trace formula. In particular, we show that the reciprocals of these $L$-functions can be approximated by very short Dirichlet polynomials, on average over $t$ and over the forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_12612 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Approximations of $SL(3,\mathbb{Z})$ Hecke-Maass $L$-Functions by short Dirichlet polynomials Kim, Jiseong Number Theory 11F30 We study averages of $L$-functions associated with Hecke-Maass cusp forms for $SL(3,\mathbb{Z})$, multiplied by Dirichlet polynomials built from the Fourier coefficients of the cusp forms. To prove this, we employ a variant of the Kuznetsov trace formula. In particular, we show that the reciprocals of these $L$-functions can be approximated by very short Dirichlet polynomials, on average over $t$ and over the forms. |
| title | Approximations of $SL(3,\mathbb{Z})$ Hecke-Maass $L$-Functions by short Dirichlet polynomials |
| topic | Number Theory 11F30 |
| url | https://arxiv.org/abs/2204.12612 |