Davide Lombardo: L-Functions, Kartoniert / Broschiert

Klappentext

• 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.