Vol. 3, No. 5, 2009

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
T-adic exponential sums over finite fields

Chunlei Liu and Daqing Wan

Vol. 3 (2009), No. 5, 489–509
Abstract

We introduce T-adic exponential sums associated to a Laurent polynomial f. They interpolate all classical pm-power order exponential sums associated to f. We establish the Hodge bound for the Newton polygon of L-functions of T-adic exponential sums. This bound enables us to determine, for all m, the Newton polygons of L-functions of pm-power order exponential sums associated to an f that is ordinary for m = 1. We also study deeper properties of L-functions of T-adic exponential sums. Along the way, we discuss new open problems about the T-adic exponential sum itself.

Keywords
$T$-adic sum, exponential sum, $L$-function, Newton polygon
Mathematical Subject Classification 2000
Primary: 11T23
Secondary: 11G25
Milestones
Received: 3 March 2008
Revised: 8 January 2009
Accepted: 9 April 2009
Published: 9 November 2009
Authors
Chunlei Liu
Department of Mathematical Sciences
Shanghai Jiao Tong University
Shanghai 200240
China
Daqing Wan
Department of Mathematics
University of California
Irvine, CA 92697-3875
United States