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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.
[PDF] Generating sequences from the sums of binomial coefficients in a .
Jacobsthal and Jacobsthal-Lucas Polynomials . Book Co., 1974. [5] W.W. Bell, Special Functions, Dover Publications, Inc. Mineola, New .
[PDF] Impulse Response Sequences and Construction of Number .
the Jacobsthal number sequence {Jn} is the IRS with respect to {1,2} . McGraw-Hill Book Co., 1976. [14] N. J. A. Sloane, My favorite .
Information Security, Coding Theory and Related Combinatorics
This book contains papers based on the fourteen lectures presented at the . Let J(n) denote the set of Jacobsthal binary sequences of length n. For k .
Gauss and Jacobi Sums - Google Books
Devised in the 19th century, Gauss and Jacobi Sums are classical formulas that form the basis for contemporary research in many of today's sciences.
[PDF] Williams, Kenneth S. (3-CARL) 击Gauss and Jacobi sums .
Until recently, the main source book for Gauss sums was H. Hasse's book . In Chapter 6, the Jacobsthal sums, which are related to Jacobi sums, are .
Gauss and Jacobi Sums, Mathematics & Statistics Books, John Wiley
Jacobsthal Sums Over Fp. Residuacity. Reciprocity Laws. Congruences for Binomial Coefficients. Diagonal Equations over Finite Fields. Gauss Sums over Fq.
[PDF] CORRESPONDING JACOBSTHAL, SUM
1. B. C. Berndt and R. J. Evans, Sums of Gauss, Jacobi, and Jacobsthal, J. Number Theory. 11 (1979), 349–398.
New Results for Certain Jacobsthal-Type Polynomials - MDPI
This paper investigates a class of Jacobsthal-type polynomials (JTPs) that involves one parameter. We present several new formulas for these polynomials.
Jacobsthal Sums - 博客來
內容簡介. The focus of this monograph is on the Jacobsthal sums of the title. These are quadratic character sums with polynomial arguments of a certain .
[PDF] On binomial transform of the generalized Jacobsthal-Padovan .
In this paper, we define the binomial transform of the generalized Jacobsthal-Padovan sequence and as special cases, the.
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