Analytic Number Theory: An Introductory Course

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World Scientific, 2004 - Mathematics - 360 pages
1 Review
This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (”elementary”) and complex variable (”analytic”) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at http: //www.math.uiuc.edu/ diamond/
 

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Contents

Section 1
1
Section 2
13
Section 3
39
Section 4
71
Section 5
87
Section 6
92
Section 7
96
Section 8
109
Section 15
183
Section 16
192
Section 17
221
Section 18
237
Section 19
261
Section 20
273
Section 21
289
Section 22
301

Section 9
111
Section 10
138
Section 11
141
Section 12
147
Section 13
163
Section 14
180
Section 23
304
Section 24
313
Section 25
339
Section 26
346
Section 27
353
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