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Problems in analytic number theory

Author: Maruti Ram Murty
Publisher: New York : Springer, ©2008.
Series: Graduate texts in mathematics, 206.; Graduate texts in mathematics., Readings in mathematics.
Edition/Format:   Print book : English : 2nd edView all editions and formats
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This informative and exhaustive study gives a problem-solving approach to the difficult subject of analytic number theory. It provides a rapid introduction to analytic methods and the ways in which  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Maruti Ram Murty
ISBN: 9780387723495 0387723498
OCLC Number: 175285192
Description: xxi, 502 pages ; 25 cm.
Contents: Problems --
Arithmetic functions --
The Möbius inversion formula and applications --
Formal Dirichlet series --
Orders of some arithmetical functions --
Average orders of arithmetical functions --
Supplementary problems --
Primes in arithmetic progressions --
Summation techniques --
Characters mod q --
Dirichlet's theorem --
Dirichlet's hyperbola method --
Supplementary problems --
The prime number theorem --
Chebyshev's theorem --
Nonvanishing of Dirichlet series on Re(s)=1 --
The Ikehara-Wiener theorem --
Supplementary problems --
The method of contour integration --
Some basic integrals --
The prime number theorem --
Further examples --
Supplementary problems --
Functional equations --
Poisson's summation formula --
The Riemann Zeta function --
Gauss sums --
Dirichlet L-functions --
Supplementary problems --
Hadamard products --
Jensen's theorem --
Entire functions of order 1 --
The gamma function --
Infinite products for [Xi](s) and [Xi](s, [Chi]) --
Zero-free regions for [Zeta](s) and L(s, [Chi]) --
Supplementary problems --
Explicit formulas --
Counting zeros --
Explicit formula for [Psi](Chi) --
Weil's explicit formula --
Supplementary problems --
The Selberg class --
The phragmén-Lindelöf theorem --
Basic properties --
Selberg's conjectures. Supplementary problems --
Sieve methods --
The Sieve of Eratosthenes --
Brun's elementary Sieve --
Selberg's Sieve --
Supplementary problems --
p-adic methods --
Ostrowski's theorem --
Hensel's Lemma --
p-adic interpolation --
The p-adic zeta-function --
Supplementary problems --
Equidistribution --
Uniform distribution modulo 1 --
Normal numbers --
Asymptotic distribution functions mod 1 --
Discrepancy --
Equidistribution and l-functions --
Supplementary problems --
Solutions --
Arithmetic functions --
The Möbius inversion formula and applications --
Formal Dirichlet series --
Orders of some arithmetical functions --
Average orders of arithmetical functions --
Supplementary problems --
Primes in arithmetic progressions --
Characters mod q --
Dirichlet's theorem --
Dirichlet's hyperbola method --
Supplementary problems --
The prime number theorem --
Chebyshev's theorem --
Nonvanishing of Dirichlet series on Re(s)=1 --
The Ikehara-Wiener theorem --
Supplementary problems --
The method of contour integration --
Some basic integrals --
The prime number theorem --
Further examples --
Supplementary problems --
Functional equations --
Poisson's summation formula --
The Riemann Zeta function --
Gauss sums --
Dirichlet l-functions --
Supplementary problems --
Hadamard products --
Jensen's theorem --
The gamma function --
Infinite products for [xi](s) and [xi](s, [chi]) --
Zero-free regions for [Zeta](s) and L(s, [Chi]) --
Supplementary problems --
Explicit formulas --
Counting zeros --
Explicit formula for [Psi]([Chi]) --
Supplementary problems --
The Selberg class --
The Phragmén-Lindelöf theorem --
Basic properties --
Selberg's conjectures --
Supplementary problems --
Sieve methods --
The Sieve of Eratosthenes --
Brun's elementary Sieve --
Selberg's Sieve --
Supplementary problems --
p-adic methods --
Ostrowski's theorem --
Hensel's Lemma --
p-adic interpolation --
The p-adic [Zeta]-function --
Supplementary problems --
Equidistribution --
Uniform distribution modulo 1 --
Normal numbers --
Asymptotic distribution functions mod 1 --
Discrepancy --
Equidistribution and L-functions --
Supplementary problems.
Series Title: Graduate texts in mathematics, 206.; Graduate texts in mathematics., Readings in mathematics.
Other Titles: Analytic number theory
Responsibility: M. Ram Murty.
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M.R. MurtyProblems in Analytic Number Theory"The reviewer strongly approves of the problem-based approach to learning, and recommends this book to any student of analytic number theory."-MATHEMATICAL Read more...

 
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