Sums of Squares of Integers
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€80.99
A01=Carlos J. Moreno
A01=Jr. Wagstaff
A01=Samuel S. Wagstaff Jr.
advanced integer representation techniques
analytic number theory
Arithmetic Progressions
Asymptotic Density
Author_Carlos J. Moreno
Author_Jr. Wagstaff
Author_Samuel S. Wagstaff Jr.
Bernoulli Numbers
Category=PBH
Category=PBV
combinatorial mathematics
cryptanalysis applications
Cusp Forms
Dirichlet Series
Eisenstein Series
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euler Product
Functional Equation
graduate level mathematics
Hardy's Theorem
Hardy’s Theorem
Hecke Operators
Irreducible Quadratic Factors
Irregular Primes
Liouville methods
Mod D2
Modular Forms
Modular Group
Nonnegative Integers
Odd Function
Odd Positive Integers
Odd Prime
Positive Integer
Quadratic Nonresidue
Quadratic Nonresidue Modulo
Quadratic Residue Modulo
Riemann Zeta Function
RSA Signature Scheme
van der Waerden theorem
Product details
- ISBN 9780367391614
- Weight: 539g
- Dimensions: 156 x 234mm
- Publication Date: 05 Sep 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares of integers for any s and n. It is also the first book to give a proof of Szemeredi's theorem, and is the first number theory book to discuss how the modern theory of modular forms complements and clarifies the classical fundamental results about sums of squares.
The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.
Moreno, Carlos J.; Wagstaff, Jr.
