On algebraic degrees of certain exponential sums over finite fields

From a complex perspective, Birch and Bombieri (1985) proposed the study of an important class of -dimensional exponential sums for , which was then generalized by Katz (1987) to general positive integer . Our previous paper (2022) enhanced the preceding work from a complex point of view and expande...

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Bibliographic Details
Published inForum mathematicum Vol. 37; no. 5; pp. 1433 - 1438
Main Author Lin, Xin
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.09.2025
Walter de Gruyter GmbH
Subjects
11L05
11T23
algebraic degree
Exponential sums
Fields (mathematics)
finite fields
Integers
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Summary:From a complex perspective, Birch and Bombieri (1985) proposed the study of an important class of -dimensional exponential sums for , which was then generalized by Katz (1987) to general positive integer . Our previous paper (2022) enhanced the preceding work from a complex point of view and expanded the subject to a -adic point of view for any positive integer . In this paper, we investigate the algebraic degree of the above exponential sum as an algebraic integer.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0933-7741
1435-5337
DOI:10.1515/forum-2024-0365