数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (6): 2419-2436.doi: 10.1007/s10473-022-0614-x

• 论文 • 上一篇    下一篇

GENERIC NEWTON POLYGON OF THE L-FUNCTION OF n VARIABLES OF THE LAURENT POLYNOMIAL I

Fusheng LENG   

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • 收稿日期:2022-07-25 出版日期:2022-12-25 发布日期:2022-12-16

GENERIC NEWTON POLYGON OF THE L-FUNCTION OF n VARIABLES OF THE LAURENT POLYNOMIAL I

Fusheng LENG   

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2022-07-25 Online:2022-12-25 Published:2022-12-16

摘要: The Hodge bound for the Newton polygon of L-functions of T-adic exponential sums associated to a Laurent polynomial is established. We improve the lower bound and study the properties of this new bound. We also study when this new bound is reached with large p arbitrarily, and hence the generic Newton polygon is determined.

关键词: exponential sum, Hodge bound, combinatorial Newton polygon

Abstract: The Hodge bound for the Newton polygon of L-functions of T-adic exponential sums associated to a Laurent polynomial is established. We improve the lower bound and study the properties of this new bound. We also study when this new bound is reached with large p arbitrarily, and hence the generic Newton polygon is determined.

Key words: exponential sum, Hodge bound, combinatorial Newton polygon

中图分类号: 

  • 11F85