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Geometry, Algebra, Number Theory, and Their Information Technology Applications by Amir Akbary, Sanoli Gun
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**About this book :- **
**Geometry, Algebra, Number Theory, and Their Information Technology Applications ** written by
** Amir Akbary, Sanoli Gun **

The purpose of this little book is to give the reader a convenient introduction to the theory of numbers, one of the most extensive and most elegant disciplines in the whole body of mathematics. The arrangement of the material is as follows:

The first five chapters are devoted to the development of those elements which are essential to any study of the subject. The sixth and last chapter is intended to give the reader some indication of the direction of further study with a brief account of the nature of the material in each of the topics suggested. The treatment throughout is made as brief as is possible consistent with clearness and is confined entirely to fundamental matters. This is done because it is believed that in this way the book may best be made to serve its purpose as an introduction to the theory of numbers.

Numerous problems are supplied throughout the text. These have been selected with great care so as to serve as excellent exercises for the student’s introductory training in the methods of number theory and to afford at the same time a further collection of useful results. The exercises marked with a star are more difficult than the others; they will doubtless appeal to the best students.

(Robert D. Carmichael)

**Book Detail :- **
** Title: ** Geometry, Algebra, Number Theory, and Their Information Technology Applications
** Edition: **
** Author(s): ** Amir Akbary, Sanoli Gun
** Publisher: **
** Series: **
** Year: **
** Pages: **
** Type: ** PDF
** Language: ** English
** ISBN: **
** Country: **

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**About Author :- **

Author ** Robert Daniel Carmichael ** (1848-1928), Associate Professor of Mathematics in Indiana University, NEW YORK.

The author ** Amir Akbary **, Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, Canada and

The author ** Sanoli Gun **, Institute of Mathematical Sciences, Chennai, Tamil Nadu, India.
This volume contains proceedings of two conferences held in Toronto (Canada) and Kozhikode (India) in 2016 in honor of the 60th birthday of Professor Kumar Murty. The meetings were focused on several aspects of number theory: The theory of automorphic forms and their associated L-functions Arithmetic geometry, with special emphasis on algebraic cycles, Shimura varieties, and explicit methods in the theory of abelian varieties The emerging applications of number theory in information technology Kumar Murty has been a substantial influence in these topics, and the two conferences were aimed at honoring his many contributions to number theory, arithmetic geometry, and information technology.

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**Book Contents :- **
**Geometry, Algebra, Number Theory, and Their Information Technology Applications ** written by
** Amir Akbary, Sanoli Gun **
cover the following topics.

Overview of the Work of Kumar Murty

On the Average Value of a Function of the Residual Index

Applications of the Square Sieve to a Conjecture of Lang and Trotter for a Pair of Elliptic Curves Over the Rationals

R-Group and Multiplicity in Restriction for Unitary Principal Series of GSpin and Spin

The 2-Class Tower of Qð

On the Bad Reduction of Certain U(2, 1) Shimura Varieties

Density Modulo 1 of a Sequence Associated with a Multiplicative Function Evaluated at Polynomial Arguments Uniqueness Results for a Class of L-Functions

Quadratic Periods of Meromorphic Forms on Punctured Riemann Surfaces

On the Local Coefficients Matrix for Coverings of SL2

Eisenstein Series of Weight One, q-Averages of the 0-Logarithm and Periods of Elliptic Curves

On Zeros of Certain Cusp Forms of Integral Weight for Full Modular Group

A Note on Burgess Bound

A Smooth Selberg Sieve and Applications

Explicit Arithmetic on Abelian Varieties

Derived Categories of Moduli Spaces of Vector Bundles on Curves II

Representations of an Integer by Some Quaternary and Octonary Quadratic Forms

A Topological Realization of the Congruence Subgroup Kernel

Fine Selmer Groups and Isogeny Invariance

Distribution of a Subset of Non-residues Modulo p

On Solving a Generalized Chinese Remainder Theorem in the Presence of Remainder Errors

Endomorphism Algebras of Abelian Varieties with Special Reference to Superelliptic Jacobians

Overview of the Work of K

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