Jacobsthal Sums
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TEORIJA ?ISEL, MATEMATI?ESKIJ ANALIZ I ICH PRILOENIJA
Author: Ivan Matveevich Vinogradov
language: en
Publisher: American Mathematical Soc.
Release Date: 1979
"This collection of paper is dedicated to Academician Ivan Matveevic̆ Vinogradov on his eighty-fifth birthday. It consists of original work on various parts of number theory, analysis, and also their applications." Title page verso.
Jacobsthal Sums
The focus of this monograph is on the Jacobsthal sums of the title. These are quadratic character sums with polynomial arguments of a certain simple form. In addition to studying Jacobsthal sums on their own, the monograph explores their role in several topics of number-theoretical interest. A prominent theme is their use in counting solutions to equations over prime fields. Another aim is to construct representations of primes as sums of squares using Jacobsthal sums. Finally, Jacobsthal sums are applied to evaluate other quadratic character sums with polynomial arguments. This text is self-contained, with minimal technical prerequisites. We have strived for an engaging exposition, incorporating numerous examples and applications, carefully selected exercises, and historical notes and perspectives. Complete solutions to all exercises are provided. This monograph should be of interest to researchers studying character sums or counting solutions to equations over finite fields, as well as to graduate students and advanced undergraduates interested in these topics.