Dissertation/Thesis Abstract

Coherent decompositions of p-adic Newton polygons for L-functions of exponential sums
by Le, Phong, Ph.D., University of California, Irvine, 2009, 68; 3355797
Abstract (Summary)

In this paper we investigate the decomposition theory for generic Newton polygons associated to L-functions of n-dimensional exponential sums over finite fields. We develop a new coherent decomposition theorem. This is a generalization of decompositions results in [15] and [17]. Our main result in this direction is a complete coherent decomposition theorem (Theorem 1.2.8).

As a demonstration of these techniques, decomposition theory is applied to a family of L-functions based on Deligne polynomials. A general formula for associated Hodge polygons as well as conditions for generic ordinarity and non-ordinarity are provided.

Indexing (document details)
Advisor: Wan, Daqing
Commitee: Rubin, Karl, Silverberg, Alice
School: University of California, Irvine
Department: Mathematics - Ph.D.
School Location: United States -- California
Source: DAI-B 70/05, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Coherent decompositions, Exponential sums, Hasse polynomials, Hodge polygons, Newton polygons, Number theory, P-adic analysis
Publication Number: 3355797
ISBN: 9781109152210
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