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Topics in Complex Analysis /
This graduate-level mathematics textbook provides an in-depth and readable exposition of selected topics in complex analysis. The material spans both the standard theory at a level suitable for a first-graduate class on the subject and several advanced topics delving deeper into the subject and appl...
| Autor principal: | |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin ; Boston :
De Gruyter,
[2023]
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| Colección: | De Gruyter Textbook
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 001 | DEGRUYTEROA_on1394871907 | ||
| 003 | OCoLC | ||
| 005 | 20240209213017.0 | ||
| 006 | m o d | ||
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| 040 | |a DEGRU |b eng |e rda |c DEGRU |d OCLCQ | ||
| 019 | |a 1394927260 |a 1396078581 | ||
| 020 | |a 9783110796810 | ||
| 020 | |a 3110796813 | ||
| 029 | 1 | |a AU@ |b 000075034207 | |
| 035 | |a (OCoLC)1394871907 |z (OCoLC)1394927260 |z (OCoLC)1396078581 | ||
| 044 | |a gw |c DE | ||
| 082 | 0 | 4 | |a 519.4 |q OCoLC |2 23/eng/20231120 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Romik, Dan, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Topics in Complex Analysis / |c Dan Romik. |
| 264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2023] | |
| 264 | 4 | |c Ã2023 | |
| 300 | |a 1 online resource (XII, 296 p.). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 0 | |a De Gruyter Textbook | |
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t 0 Prerequisites and notation -- |t 1 Basic theory -- |t 2 The prime number theorem -- |t 3 Conformal mapping -- |t 4 Elliptic functions -- |t 5 Modular forms -- |t 6 Sphere packing in 8 dimensions -- |t A Appendix: Background on sphere packings -- |t Bibliography -- |t Web Bibliography -- |t Index |
| 520 | |a This graduate-level mathematics textbook provides an in-depth and readable exposition of selected topics in complex analysis. The material spans both the standard theory at a level suitable for a first-graduate class on the subject and several advanced topics delving deeper into the subject and applying the theory in different directions. The focus is on beautiful applications of complex analysis to geometry and number theory. The text is accompanied by beautiful figures illustrating many of the concepts and proofs. Among the topics covered are asymptotic analysis; conformal mapping and the Riemann mapping theory; the Euler gamma function, the Riemann zeta function, and a proof of the prime number theorem; elliptic functions, and modular forms. The final chapter gives the first detailed account in textbook format of the recent solution to the sphere packing problem in dimension 8, published by Maryna Viazovska in 2016 - a groundbreaking proof for which Viazovska was awarded the Fields Medal in 2022. The book is suitable for self-study by graduate students or advanced undergraduates with an interest in complex analysis and its applications, or for use as a textbook for graduate mathematics classes, with enough material for 2-3 semester-long classes. Researchers in complex analysis, analytic number theory, modular forms, and the theory of sphere packing, will also find much to enjoy in the text, including new material not found in standard textbooks. | ||
| 546 | |a In English. | ||
| 588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Aug 2023). | |
| 590 | |a De Gruyter Online |b De Gruyter Open Access eBooks | ||
| 650 | 4 | |a Asymptotische Analyse. | |
| 650 | 4 | |a Das Euler-Gamma und Riemannsche Zetafunktionen. | |
| 650 | 4 | |a Elliptische Funktionen. | |
| 650 | 4 | |a Kugelpackung. | |
| 650 | 4 | |a Modulare Formen. | |
| 653 | |a Complex analysis, analytic functions, complex integration, complex variables,. | ||
| 776 | 0 | |c EPUB |z 9783110796889 | |
| 776 | 0 | |c print |z 9783110796780 | |
| 856 | 4 | 0 | |u https://www.degruyter.com/openurl?genre=book&isbn=9783110796810 |z Texto completo |
| 938 | |a De Gruyter |b DEGR |n 9783110796810 | ||
| 938 | |a De Gruyter |b DEGR |n 9783110796810 | ||
| 994 | |a 92 |b IZTAP | ||