L-FUNCTIONS OF SYMMETRIC POWERS OF THE GENERALIZED AIRY FAMILY OF EXPONENTIAL SUMS-Reference-Cited by-同舟云学术

L-FUNCTIONS OF SYMMETRIC POWERS OF THE GENERALIZED AIRY FAMILY OF EXPONENTIAL SUMS

Published:2011-12 Issue:08 Volume:07 Page:2019-2064
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

HAESSIG C. DOUGLAS¹,ROJAS-LEÓN ANTONIO²

Affiliation:

1. Department of Mathematics, University of Rochester, Rochester, NY, USA

2. Departamento de Álgebra, Universidad de Sevilla, Sevilla, Spain

Abstract

This paper looks at the L-function of the kth symmetric power of the [Formula: see text]-sheaf Ai f over the affine line [Formula: see text] associated to the generalized Airy family of exponential sums. Using ℓ-adic techniques, we compute the degree of this rational function as well as the local factors at infinity. Using p-adic techniques, we study the q-adic Newton polygon of the L-function.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042111005040

Reference29 articles.

1. A p-adic theory of Hecke polynomials

2. Newton polyhedra and the degree of theL-function associated to an exponential sum

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