Header

UZH-Logo

Maintenance Infos

Additive decompositions induced by multiplicative characters over finite fields


Michele, Elia; Schipani, Davide (2012). Additive decompositions induced by multiplicative characters over finite fields. In: Lavrauw, Michel; Mullen, Garry L; Nikova, Svetla; Panario, Daniel; Storme, Leo. Theory and applications of finite fields. Providence, Rhode Island: American Mathematical Society, 179-186.

Abstract

In 1952, Perron showed that quadratic residues in a field of prime order satisfy certain additive properties. This result has been generalized in different directions, and our contribution is to provide a further generalization concerning multiplicative quadratic and cubic characters over any finite field. In particular, recalling that a character partitions the multiplicative group of the field into cosets with respect to its kernel, we will derive the number of representations of an element as a sum of two elements belonging to two given cosets. These numbers are then related to the equations satisfied by the polynomial characteristic functions of the cosets.
Further, we show a connection, a quasi-duality, with the problem of determining how many elements can be added to each element of a subset of a coset in such a way as to obtain elements still belonging to a subset of a coset.

Abstract

In 1952, Perron showed that quadratic residues in a field of prime order satisfy certain additive properties. This result has been generalized in different directions, and our contribution is to provide a further generalization concerning multiplicative quadratic and cubic characters over any finite field. In particular, recalling that a character partitions the multiplicative group of the field into cosets with respect to its kernel, we will derive the number of representations of an element as a sum of two elements belonging to two given cosets. These numbers are then related to the equations satisfied by the polynomial characteristic functions of the cosets.
Further, we show a connection, a quasi-duality, with the problem of determining how many elements can be added to each element of a subset of a coset in such a way as to obtain elements still belonging to a subset of a coset.

Statistics

Altmetrics

Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2012
Deposited On:07 Dec 2016 08:12
Last Modified:07 Dec 2016 08:17
Publisher:American Mathematical Society
Series Name:Contemporary Mathematics
Number:579
ISSN:0271-4132
ISBN:978-0-8218-5298-9 (print); 978-0-8218-9157-5 (online)
Publisher DOI:https://doi.org/10.1090/conm/579
Related URLs:http://www.recherche-portal.ch/ZAD:default_scope:ebi01_prod010176608 (Library Catalogue)

Download

Full text not available from this repository.
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations