Description

Book Synopsis

- 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.

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    A Paperback by Davide Lombardo

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      Publisher: Springer
      Publication Date: Publication Date: 5/4/2025
      ISBN13: 9783031851445, 978-3031851445
      ISBN10: 3031851447

      Description

      Book Synopsis

      - 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.

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