Newton polygons for certain two variable exponential sums
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910699500863488 |
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| author | Wei, Bolun |
| author_facet | Wei, Bolun |
| contents | We studies the Newton polygon for the L-function of toric exponential sums attached to a family of two variable generalized hyperkloosterman sum,$f_{t}(x,y)=x^{n}+y+\frac{t}{xy}$ with $t$ the parameter. The explicit Newton polygon is obtained by systematically using Dwork's $θ_{\infty}$-splitting function with an appropriate choice of basis for cohomology following the method of Adolphson and Sperber[2]. Our result provides a non-trivial explicit Newton polygon for a non-ordinary family of more than one variable with asymptotical behavior, which gives an evidence of Wan's limit conjecture[15]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09977 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Newton polygons for certain two variable exponential sums Wei, Bolun Number Theory We studies the Newton polygon for the L-function of toric exponential sums attached to a family of two variable generalized hyperkloosterman sum,$f_{t}(x,y)=x^{n}+y+\frac{t}{xy}$ with $t$ the parameter. The explicit Newton polygon is obtained by systematically using Dwork's $θ_{\infty}$-splitting function with an appropriate choice of basis for cohomology following the method of Adolphson and Sperber[2]. Our result provides a non-trivial explicit Newton polygon for a non-ordinary family of more than one variable with asymptotical behavior, which gives an evidence of Wan's limit conjecture[15]. |
| title | Newton polygons for certain two variable exponential sums |
| topic | Number Theory |
| url | https://arxiv.org/abs/2411.09977 |