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Many areas of active research within the broad field of number theory relate to properties of polynomials, and this volume displays the most recent and most interesting work on this theme. The 2006 Number Theory and Polynomials workshop in Bristol drew together international researchers with a variety of number-theoretic interests, and the book’s contents reflect the quality of the meeting. Topics covered include recent work on the Schur-Siegel-Smyth trace problem, Mahler measure and its generalisations, the merit factor problem, Barker sequences, K3-surfaces, self-inversive polynomials, Newman’s inequality, algorithms for sparse polynomials, the integer transfinite diameter, divisors of polynomials, non-linear recurrence sequences, polynomial ergodic averages, and the Hansen-Mullen primitivity conjecture. With surveys and expository articles presenting the latest research, this volume is essential for graduates and researchers looking for a snapshot of current progress in polynomials and number theory.• An invaluable resource to both students and experts in this area, with survey articles on the most important topics in the field • Expository articles introduce graduate students to some problems of active interest • The inclusion of new results from leading experts in the field provides a snapshot of current progress

From their inception, Siegel modular forms have been studied extensively because of their significance in both automorphic functions in several complex variables and number theory. The comprehensive theory of automorphic forms to subgroups of algebraic groups and the arithmetical theory of modular forms illustrate these two aspects in an illuminating manner. The author’s aim is to present a straightforward and easily accessible survey of the main ideas of the theory at an elementary level, providing a sound basis from which the reader can study advanced works and undertake original research. This book is based on lectures given by the author for a number of years and is intended for a one-semester graduate course, though it can also be used profitably for self-study. The only prerequisites are a basic knowledge of algebra, number theory and complex analysis.Contents

Preface; 1. The modular group; 2. Basic facts on modular forms; 3. Large weights; 4. Small weights; 5. Modular functions; 6. Dirichlet series; Bibliography; Index.

Number theory : A Computational Introduction to Number Theory and Algebra - Victor Shoup A Concise Introduction to the Theory of Numbers- Baker A. A Course in Arithmetic (graduate level) - J. Serre A course in computational algebraic number theory - Cohen H. A Course in Number Theory and Cryptography 2 ed - Neal Koblitz A Course In Number Theory And Cryptography 2Ed - Koblitz N Advanced Number Theory - Cohn Algebra and number theory - Baker A. Algebraic Groups and Number Theory - Platonov & Rapinchuk Algebraic Number Theory - IYANAGA ALGEBRAIC NUMBER THEORY - MILNE Algorithmic Methods In Algebra And Number Theory - Pohst M Algorithmic number theory - Cohen H. Algorithmic number theory, vol. 1 Efficient algorithms - Bach E., Shallit J. An Explicit Approach To Elementary Number Theory - stein An Introduction to Conformal Field Theory [jnl article] - M. Gaberdiel AN INTRODUCTION TO THE THEORY OF NUMBERS - hardy & wright An Introduction to the Theory of Numbers - Leo Moser An introduction to the theory of numbers 5ed - Niven I., Zuckerman H.S., Montgomery H.L. Analytic number theory - Iwaniec H.,Kowalski E. Analytic Number Theory - Newman D.J. Analytic Number Theory- Jia & Matsumoto Arithmetic Theory of Elliptic Curves - J. Coates Computational Algebraic Number Theory - Pohst M E Computational excursions in analysis and number theory - Borwein P.

Only Problems Not Solutions - F. Smarandache Prime Numbers The Most Mysterious Figures in Math - D. Wells Problems In Algebraic Number Theory 2Ed - Murty M , Esmonde J SOlved and unsolved problems in Number Theory - Daniel Shanks Surfing on the Ocean of Numbers - H. Ibstedt Survey Of Diophantine Geometry - Serge Lang The elements of the theory of algebraic numbers - Hilbert.djv The Foundations of Arithmetic 2nd ed. revised - G. Frege The New Book Of Prime Number Records 3rd ed. - P. Ribenboim The Theory of algebraic numbers sec ed - Pollard H., Diamond H.G. the theory of functions and sets of natural numbers - Odifreddi, P Three Pearls of Number Theory - Khinchin Transcendental number theory - Baker A. Unsolved Problems In Number Theory 2 Ed - R K Guy.djv

Introduction to Modern Number Theory Fundamental Problems, Ideas and Theories 2nd Edition - Manin I., Panchishkin A Introduction to p-adic numbers and valuation theory- Bachman G. Introduction to the Theory of Numbers 4th ed. - G. Hardy, E. Wright Lectures on topics in algebraic number theory - Ghorpade Mainly Natural Numbers - Studies on Sequences - H. Ibstedt Math. problems and proofs combinatorics, number theory and geometry - B. Kisacanin Mathematical Problems And Proofs Combinatorics, Number Theory, and Geometry - Kluwer Academic My Numbers, My Friends - Popular Lectures on Number Theory My Numbers,My Friends Popular Lectures On Number Theory - Ribenboim Number Theory - Z.Borevitch, I. Shafarevich Number theory for beginners - Weil A. Number theory for computing - Yan S Y. Numerical Mathematics - A. Quarteroni, A. Sacco, F. Saleri Numerical Methods for Engineers and Scientists 2nd ed. - J. Hoffman Numerical Optimization - J. Nocedal, S. Wright Numerical Recipes in C - The Art Of Scientific Computing 2nd ed. Numerical Recipes in Fortran 77 2nd ed. Vol 1 Old And New Problems And Results In Combinatorial Number Theory - Erdos, P.&Graham, R.L

Topics in Harmonic Analysis and Ergodic Theory Joseph M. Rosenblatt, Alexander M. Stokolos, Ahmed I. Zayed ISBN: 0821842358 Paperback American Mathematical Society Usually despatched within 3 to 9 days

There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. The breakthrough achieved by Tao and Green is attributed to applications of techniques from ergodic theory and harmonic analysis to problems in number theory.Articles in the present volume are based on talks delivered by plenary speakers at a conference on Harmonic Analysis and Ergodic Theory (DePaul University, Chicago, December 2-4, 2005). Of ten articles, four are devoted to ergodic theory and six to harmonic analysis, although some may fall in either category. The articles are grouped in two parts arranged by topics. Among the topics are ergodic averages, central limit theorems for random walks, Borel foliations, ergodic theory and low pass filters, data fitting using smooth surfaces, Nehari's theorem for a polydisk, uniqueness theorems for multi-dimensional trigonometric series, and Bellman and s-functions.In addition to articles on current research topics in harmonic analysis and ergodic theory, this book contains survey articles on convergence problems in ergodic theory and uniqueness problems on multi-dimensional trigonometric series.