L-Functions An Elementary Introduction /
This book provides an accessible introduction to the theory of L-functions, emphasising their central role in number theory and their direct applications to key results. Designed to be elementary, it offers readers a clear pathway into the subject, starting from minimal background. It describes seve...
Gardado en:
| Autor Principal: | |
|---|---|
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | inglés |
| Publicado: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
|
| Edición: | 1st ed. 2025. |
| Series: | La Matematica per il 3+2,
171 |
| Subjects: | |
| Acceso en liña: | https://doi.org/10.1007/978-3-031-85145-2 |
| Tags: |
Engadir etiqueta
Sen Etiquetas, Sexa o primeiro en etiquetar este rexistro!
|
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-031-85145-2 | ||
| 003 | DE-He213 | ||
| 005 | 20260906084024.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 250427s2025 sz | o |||| 0|eng d | ||
| 020 | |a 9783031851452 |9 978-3-031-85145-2 | ||
| 024 | 7 | |a 10.1007/978-3-031-85145-2 |2 doi | |
| 050 | 4 | |a QA241-247.5 | |
| 072 | 7 | |a PBH |2 bicssc | |
| 072 | 7 | |a MAT022000 |2 bisacsh | |
| 072 | 7 | |a PBH |2 thema | |
| 082 | 0 | 4 | |a 512.7 |2 23 |
| 100 | 1 | |a Lombardo, Davide. |e author. |0 (orcid)0000-0002-1069-3379 |1 https://orcid.org/0000-0002-1069-3379 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a L-Functions |h [electronic resource] : |b An Elementary Introduction / |c by Davide Lombardo. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2025. | |
| 300 | |a 1 online resource (XIV, 261 p. 4 illus.). |b 1 illus. in color. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
| 341 | 0 | |b Use of colour is Not sole means of conveying information |2 onix | |
| 341 | 0 | |b Use of high contrast between text and background colour |2 onix | |
| 341 | 0 | |b Next / Previous structural navigation |2 onix | |
| 341 | 0 | |b All Non-decorative content supports reading without sight |2 onix | |
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a La Matematica per il 3+2, |x 2038-5757 ; |v 171 | |
| 505 | 0 | |a - Part I Classical -functions and applications -- 1. What is an -function? -- 2. The Prime Number Theorem -- 3. Review of Algebraic Number Theory -- 4. A Primer of Representation Theory -- 5. The -Function of a Complex Galois Representation -- 6. Dirichlet’s Theorem on Arithmetic Progressions -- 7. The Chebotarev Density Theorem -- Part II Prerequisites for Tate’s Thesis -- 8. The Haar Measure -- 9. Abstract Fourier Analysis -- 10. Review of Local Fields -- 11. Restricted Direct Products -- Part III Tate’s Thesis -- 12. The Local Theory -- 13. The Global Theory -- 14. Hecke -Functions -- 15. Recovering the Classical Theory -- 16. An Extended Example: the -Function of a CM Elliptic Curve. | |
| 520 | |a This book provides an accessible introduction to the theory of L-functions, emphasising their central role in number theory and their direct applications to key results. Designed to be elementary, it offers readers a clear pathway into the subject, starting from minimal background. It describes several important classes of L-functions — Riemann and Dedekind zeta functions, Dirichlet L-functions, and Hecke L-functions (for characters with finite image) — by showing how they are all special cases of the construction, due to Artin, of the L-function of a Galois representation. The analytic properties of abelian L-functions are presented in detail, including the full content of Tate's thesis, which establishes analytic continuation and functional equations via harmonic analysis. General Hecke L-functions are also discussed, using the modern perspective of idèles and adèles to connect their analytic theory with the representation-theoretic approach of Artin's L-functions. A distinguishing feature of this book is its accessibility: while largely avoiding arithmetic geometry, it provides introductions to both algebraic number theory and key aspects of representation theory. This approach ensures that the material is accessible to both beginning graduate students and advanced undergraduates. Applications play a central role throughout, highlighting how L-functions underpin significant results in number theory. The book provides complete proofs of the prime number theorem, Dirichlet's theorem on primes in arithmetic progressions, Chebotarev's density theorem, and the analytic class number formula, demonstrating the power of the theory in solving classical problems. It serves as an ideal introduction for advanced undergraduates and beginning graduate students and can also be a useful reference for preparing a course on the subject. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Number theory. | |
| 650 | 1 | 4 | |a Number Theory. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783031851445 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031851469 |
| 830 | 0 | |a La Matematica per il 3+2, |x 2038-5757 ; |v 171 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-85145-2 |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 912 | |a ZDB-2-251 | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||
| 950 | |a Focus Bundle Mathematics and Statistics (SpringerNature-85421) | ||