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...
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| Format: | Electrònic eBook |
| Idioma: | anglès |
| Publicat: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
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| Edició: | 1st ed. 2025. |
| Col·lecció: | La Matematica per il 3+2,
171 |
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| Accés en línia: | https://doi.org/10.1007/978-3-031-85145-2 |
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Taula de continguts:
- - Part I Classical 𝑳-functions and applications
- 1. What is an 𝑳-function?
- 2. The Prime Number Theorem
- 3. Review of Algebraic Number Theory
- 4. A Primer of Representation Theory
- 5. The 𝑳-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 𝑳-Functions
- 15. Recovering the Classical Theory
- 16. An Extended Example: the 𝑳-Function of a CM Elliptic Curve.