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Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis

Hugh L. Montgomery University of Michigan, Ann Arbor, MI
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-0-8218-0737-8
Product Code: CBMS/84
List Price: $41.00 Individual Price:$32.80
Electronic ISBN: 978-1-4704-2444-2
Product Code: CBMS/84.E
List Price: $38.00 Individual Price:$30.40
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List Price: $61.50 Click above image for expanded view Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis Hugh L. Montgomery University of Michigan, Ann Arbor, MI A co-publication of the AMS and CBMS Available Formats:  Softcover ISBN: 978-0-8218-0737-8 Product Code: CBMS/84  List Price:$41.00 Individual Price: $32.80  Electronic ISBN: 978-1-4704-2444-2 Product Code: CBMS/84.E  List Price:$38.00 Individual Price: $30.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$61.50
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 841994; 220 pp
MSC: Primary 11; 42;

This book contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. This book would be an excellent resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in number theory.

Analytic number theorists and harmonic analysts.

• Chapters
• 1. Uniform distribution (chapter 1)
• 2. van der Corput sets (chapter 2)
• 3. Exponential sums. I: The methods of Weyl and van der Corput (chapter 3)
• 4. Exponential sums. II: Vinogradov’s method (chapter 4)
• 5. An introduction to Turan’s method (chapter 5)
• 6. Irregularities of distribution (chapter 6)
• 7. Mean and large values of Dirichlet polynomials (chapter 7)
• 8. Distribution of reduced residue classes in short intervals (chapter 8)
• 9. Zeros of L-functions (chapter 9)
• 10. Small polynomials with integral coefficients (chapter 10)
• 11. Some unsolved problems (appendix)
• Reviews

• The book is a masterpiece of exposition and can be highly recommended to anybody interested in the connections of analysis and number theory.

Zentralblatt MATH
• Many analysts, not necessarily specialists in harmonic analysis, will be able to find much to interest them here … The long lists of references provided for each chapter are one of the invaluable features of a very readable and stimulating book.

Bulletin of the LMS
• These lectures give a lively, often original, look at a selection of topics from the area described by the title and, once one accepts the restriction of the previous sentence, there is nobody, anywhere, better equipped to tell this tale … this book deserves the attention of every analytic number theorist …adds considerably more to the literature than a number of books which could serve that function.

Mathematical Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 841994; 220 pp
MSC: Primary 11; 42;

This book contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. This book would be an excellent resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in number theory.

Analytic number theorists and harmonic analysts.

• Chapters
• 1. Uniform distribution (chapter 1)
• 2. van der Corput sets (chapter 2)
• 3. Exponential sums. I: The methods of Weyl and van der Corput (chapter 3)
• 4. Exponential sums. II: Vinogradov’s method (chapter 4)
• 5. An introduction to Turan’s method (chapter 5)
• 6. Irregularities of distribution (chapter 6)
• 7. Mean and large values of Dirichlet polynomials (chapter 7)
• 8. Distribution of reduced residue classes in short intervals (chapter 8)
• 9. Zeros of L-functions (chapter 9)
• 10. Small polynomials with integral coefficients (chapter 10)
• 11. Some unsolved problems (appendix)
• The book is a masterpiece of exposition and can be highly recommended to anybody interested in the connections of analysis and number theory.

Zentralblatt MATH
• Many analysts, not necessarily specialists in harmonic analysis, will be able to find much to interest them here … The long lists of references provided for each chapter are one of the invaluable features of a very readable and stimulating book.

Bulletin of the LMS
• These lectures give a lively, often original, look at a selection of topics from the area described by the title and, once one accepts the restriction of the previous sentence, there is nobody, anywhere, better equipped to tell this tale … this book deserves the attention of every analytic number theorist …adds considerably more to the literature than a number of books which could serve that function.

Mathematical Reviews
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.