Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. <P>The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
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"The book is written in a very lively and nicely readable style ... contains a very well chosen and balanced material." ---- EMS Newsletter
"The authors are active researchers with a lot of experience and deep insight, and their creative attitude makes reading particularly rewarding... It can be warmly recommended toa wide readership ..." ---- Zentralblatt Math
"The authors are active researchers with a lot of experience and deep insight, and their creative attitude makes reading particularly rewarding... It can be warmly recommended toa wide readership ..." ---- Zentralblatt Math
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4 of 5 people found the following review helpful:
4.0 out of 5 stars
Great Reference,
By Paul "Paul" (USA) - See all my reviews
This review is from: Analytic Number Theory (Colloquium Publications, Vol. 53) (Colloquium Publications (Amer Mathematical Soc)) (Hardcover)
This book covers an amazing amount of material and is an extremely good reference, going from more classical topics to spectral methods of automorphic forms and even mentioning the GUE hypothesis and the distribution of zeroes of L-functions. But this is not a book for average beginners or for self-study, as many of the proofs contain next to no detail.
2 of 4 people found the following review helpful:
3.0 out of 5 stars
Good reference, awful textbook,
By
This review is from: Analytic Number Theory (Colloquium Publications, Vol. 53) (Colloquium Publications (Amer Mathematical Soc)) (Hardcover)
The authors (especially the first-named author, on whose course notes the book is based) are some of the best people in the field, and the book contains a wealth of information, but the organization is, um, non-existent -- results in section a.b might require results in section a+N.b+M at best, and something the authors thought about ten years ago at worst, some of the more interesting results are hidden in the exercises, etc, etc. So, if you are learning the field, DO get it, but don't try too hard to read it.
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Inside This Book
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First Sentence:
Throughout this book Z, Q, R, C denote the sets of integers, rationals, real and complex numbers respectively. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
short character sums, convexity hound, constant being absolute, implied constant depending, primitive cusp form, analytic conductor, classical cusp forms, exceptional zero, implied constant depends, flecke operators, large sieve inequality, absolute implied, class group character, sums over finite fields, large sieve inequalities, squarefree numbers, real primitive character, convexity bound, exponent pair, critical zeros, exponential suns, general bilinear forms, error terni, standard fundamental domain, trivial estimation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Dirichlet L-functions, Hecke L-function, Artin L-functions, Weyl Criterion, Rankin-Selberg L-functions, Therefore Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Throughout this book Z, Q, R, C denote the sets of integers, rationals, real and complex numbers respectively. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
short character sums, convexity hound, constant being absolute, implied constant depending, primitive cusp form, analytic conductor, classical cusp forms, exceptional zero, implied constant depends, flecke operators, large sieve inequality, absolute implied, class group character, sums over finite fields, large sieve inequalities, squarefree numbers, real primitive character, convexity bound, exponent pair, critical zeros, exponential suns, general bilinear forms, error terni, standard fundamental domain, trivial estimation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Dirichlet L-functions, Hecke L-function, Artin L-functions, Weyl Criterion, Rankin-Selberg L-functions, Therefore Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 6
books:
See all 6 books this book cites
- Discrete Subgroups of Semisimple Lie Groups (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 3 Folge) by Grigorii A. Margulis in Back Matter
- Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang in Back Matter
- Collected Papers Vol 2 by Atle Selberg in Back Matter
- Number Theory: An approach through history from Hammurapi to Legendre by André Weil in Back Matter
- Transcendental Number Theory (Cambridge Mathematical Library) by Alan Baker in Back Matter
See all 6 books this book cites
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