Analytic Number Theory for Undergraduates Monographs In Number Theory

Name: Analytic Number Theory for Undergraduates Monographs In Number Theory
Price: 19.04 USD
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ISBN: 9789814271363

ISBN-10: 9814271365

ISBN-13: 9789814271363

Edition: 2009

Authors: Heng Huat Chan, Heng Huat Chan

List price: $33.00

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Description:

This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression. The materials in this book are based on A Hidebrand's 1991 lectures delivered at the University of Illinois at Urbana-Champaign and the author's course conducted at the National University of Singapore from 2001 to 2008.

Book details

List price: $33.00
Copyright year: 2009
Publisher: World Scientific Publishing Co Pte Ltd
Publication date: 5/1/2009
Binding: Paperback
Pages: 200
Size: 5.75" wide x 9.25" long x 0.50" tall
Weight: 0.550
Language: English



Preface



The Fundamental Theorem of Arithmetic



Least Integer Axiom and Mathematical Induction



Division Alogrithm



Greatest common divisors



The Euclidean Algorithm



Congruences



Fundamental Theorem of Arithmetic



Exercises



Arithmetical Functions and Dirichlet Multiplication



The M&oumlet;bius function



The Euler totient function



Dirichlet product



Dirichlet inverses and the M&oumlet;bius inversion formula



Multiplicative functions and Dirichlet products



Exercises



Averages of Arithmetical Functions



Introduction



Partial Summation and the Euler-Maclaurin summation formula



Some elementary asymptotic formulas



The divisor function and Dirichlet's hyperbola method



An application of the hyperbola method



Exercises



Elementary Results on the Distribution of Primes



Introduction



The function ï¿½(x)



The functions ï¿½(x) and ï¿½(x)



Merten's estimates



Prime Number Theorem and M(ï¿½)



The Bertrand Postulate



Exercises



The Prime Number Theorem



The Prime Number Theorem



The Riemann zeta function



Euler's product and the product representation of ï¿½(s)



Analytic continuation of ï¿½ to ï¿½>0



Upper bounds for ï¿½(s) and ï¿½'(s) near ï¿½=1



The non-vanishing of ï¿½(1+it)



A lower bound for ï¿½(s) near ï¿½=1



Perron's Formula



Completion of the proof of the Prime Number Theorem



Exercises



Dirichlet Series



Absolute convergence of a Dirichlet series



The Uniqueness Theorem



Multiplication of Dirichlet series



Conditional convergence of Dirichlet series



Landau's Theorem for Dirichlet series



Exercises



Primes in Arithmetic Progression



Introduction



Dirichlet's characters



The orthogonal relations



The Dirichlet L-series



Proof of Dirichlet's Theorem



Exercises


Bibliography


Notation


Index