Newton polygons for certain two variable exponential sums

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 \(\theta_{\infty...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Author: Bolun Wei
Format: Article
Language:English
Subjects:
Homology
Polygons
Online Access:Get full text
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Summary: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 \(\theta_{\infty}\)-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].
ISSN:2331-8422