Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (6): 2419-2436.doi: 10.1007/s10473-022-0614-x

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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

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

CLC Number: 

  • 11F85
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