A course in analytic number theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2014
|
| Schriftenreihe: | Graduate studies in mathematics
160 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 341-356 |
| Beschreibung: | XVIII, 371 S. graph. Darst. |
| ISBN: | 9781470417062 |
Internformat
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| 245 | 1 | 0 | |a A course in analytic number theory |c Marius Overholt |
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Datensatz im Suchindex
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| adam_text | Titel: A course in analytic number theory
Autor: Overholt, Marius
Jahr: 2014
Contents Preface xi Acknowledgments xiii How to use this text xv Introduction xvii Chapter 1. Arithmetic Functions 1 §1.1. The method of Chebyshev 1 §1.2. Bertrand’s Postulate 6 §1.3. Simple estimation techniques 7 §1.4. The Mertens estimates 10 §1.5. Sums over divisors 16 §1.6. The hyperbola method 21 §1.7. Notes 27 Exercises 33 Chapter 2. Topics on Arithmetic Functions 41 §2.1. * The neighborhood method 41 §2.2. * The normal order method 46 §2.3. * The Mertens function 49 §2.4. Notes 55 Exercises 56 vii
Contents viii Chapter 3. Characters and Euler Products §3.1. The Euler product formula §3.2. Convergence of Dirichlet series §3.3. Harmonics §3.4. Group representations §3.5. Fourier analysis on finite groups §3.6. Primes in arithmetic progressions §3.7. Gauss sums and primitive characters §3.8. * The character group §3.9. Notes Exercises Chapter 4. The Circle Method §4.1. Diophantine equations §4.2. The major arcs §4.3. The singular series §4.4. Weyl sums §4.5. An asymptotic estimate §4.6. Notes Exercises Chapter 5. The Method of Contour Integrals §5.1. The Perron formula §5.2. Bounds for Dirichlet L-functions §5.3. Notes Exercises Chapter 6. The Prime Number Theorem §6.1. A zero-free region §6.2. A proof of the PNT §6.3. Notes Exercises Chapter 7. The Siegel-Walfisz Theorem §7.1. Zero-free regions for L-functions §7.2. An idea of Landau §7.3. The theorem of Siegel §7.4. The Borel-Carathéodory lemma 59 59 64 67 71 76 83 89 95 99 103 111 111 116 123 130 138 144 150 157 157 162 165 166 169 169 173 177 179 183 183 190 193 196
Contents ix §7.5. The PNT for arithmetic progressions §7.6. Notes Exercises Chapter 8. Mainly Analysis §8.1. The Poisson summation formula §8.2. Theta functions §8.3. The gamma function §8.4. The functional equation of £(s) §8.5. * The functional equation of L(s, x) §8.6. The Hadamard factorization theorem §8.7. * The Phragmen-Lindelof principle §8.8. Notes Exercises Chapter 9. Euler Products and Number Fields §9.1. The Dedekind zeta function §9.2. The analytic class number formula §9.3. * Class numbers of quadratic fields §9.4. * A discriminant bound §9.5. * The Prime Ideal Theorem §9.6. * A proof of the Ikehara theorem §9.7. Induced representations §9.8. Artin L-functions §9.9. Notes Exercises Chapter 10. Explicit Formulas §10.1. The von Mangoldt formula §10.2. The primes and RH §10.3. The Guinand-Weil formula §10.4. Notes Exercises Chapter 11. Supplementary Exercises Exercises Solutions 198 205 205 209 209 216 223 227 231 235 240 243 247 255 255 262 269 275 281 287 293 296 302 303 307 307 314 315 322 324 327 327 330
X Contents Bibliography 341 List of Notations 357 Index 363
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| isbn | 9781470417062 |
| language | English |
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| spelling | Overholt, Marius 1957- Verfasser (DE-588)1066395756 aut A course in analytic number theory Marius Overholt Providence, RI American Math. Soc. 2014 XVIII, 371 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 160 Literaturverz. S. 341-356 Analytische Zahlentheorie (DE-588)4001870-2 gnd rswk-swf Analytische Zahlentheorie (DE-588)4001870-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2041-3 Graduate studies in mathematics 160 (DE-604)BV009739289 160 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027773995&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Overholt, Marius 1957- A course in analytic number theory Graduate studies in mathematics Analytische Zahlentheorie (DE-588)4001870-2 gnd |
| subject_GND | (DE-588)4001870-2 |
| title | A course in analytic number theory |
| title_auth | A course in analytic number theory |
| title_exact_search | A course in analytic number theory |
| title_full | A course in analytic number theory Marius Overholt |
| title_fullStr | A course in analytic number theory Marius Overholt |
| title_full_unstemmed | A course in analytic number theory Marius Overholt |
| title_short | A course in analytic number theory |
| title_sort | a course in analytic number theory |
| topic | Analytische Zahlentheorie (DE-588)4001870-2 gnd |
| topic_facet | Analytische Zahlentheorie |
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