MARC details
| 000 -LEADER |
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| fixed length control field |
02567cam a2200277 i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
137676 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
ISI Library, Kolkata |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20170517115556.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
160525s2016 riu b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781470430450 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
ISI Library |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
510MS |
| Edition number |
23 |
| Item number |
Am512 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Diamond, Harold G., |
| Relator term |
author |
| 245 10 - TITLE STATEMENT |
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| Title |
Beurling generalized numbers / |
| Statement of responsibility, etc |
Harold G. Diamond, Wen-Bin Zhang (Cheung Man Ping). |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Providence : |
| Name of publisher, distributor, etc |
American Mathematical Society, |
| Date of publication, distribution, etc |
©2016. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xi, 244 pages ; |
| Dimensions |
26 cm. |
| 490 0# - SERIES STATEMENT |
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| Series statement |
Mathematical surveys and monographs ; |
| Volume number/sequential designation |
v 213. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1. Overview --<br/>2. Analytic machinery --<br/>3. dN as an exponential and Chebyshevs's identity --<br/>4. Upper and lower estimates of N (x) --<br/>5. Mertens' formulas and logarithmic density --<br/>6. O-Density of g-integers --<br/>7. Density of g-integers --<br/>8. Simple estimates of pie (x) --<br/>9. Chebyshev bounds-elementary theory --<br/>10. Wiener-Ikehara tauberian theorems --<br/>11. Chebyshev bounds-analytic methods --<br/>12. Optimality of a Chebyshev bound --<br/>13. Beurling's PNT --<br/>14. Equivalences to th PNT --<br/>15. Kahane's PNT --<br/>16. PNT with remainder --<br/>17. Optimality of the dIVP remainder term --<br/>18. The Dickman and Buchstab functions. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
Generalized numbers" is a multiplicative structure introduced by A. Beurling to study how independent prime number theory is from the additivity of the natural numbers. The results and techniques of this theory apply to other systems having the character of prime numbers and integers; for example, it is used in the study of the prime number theorem (PNT) for ideals of algebraic number fields. Using both analytic and elementary methods, this book presents many old and new theorems, including several of the authors' results, and many examples of extremal behavior of g-number systems. Also, the authors give detailed accounts of the $L^2$ PNT theorem of J. P. Kahane and of the example created with H. L. Montgomery, showing that additive structure is needed for proving the Riemann hypothesis. Other interesting topics discussed are propositions "equivalent" to the PNT, the role of multiplicative convolution and Chebyshev's prime number formula for g-numbers, and how Beurling theory provides an interpretation of the smooth number formulas of Dickman and de Bruijn. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Prime numbers. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Real numbers. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Riemann hypothesis. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Zhang, Wen-Bin, |
| Relator term |
author |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Books |
