Spectral methods of automorphic forms. 2nd ed. (English) Zbl 1006.11024
Graduate Studies in Mathematics. 53. Providence, RI: American Mathematical Society (AMS). Madrid: Revista Matemática Iberoamericana, xi, 220 p. (2002).
The book under review is the second edition of the monograph “Introduction to the spectral theory of automorphic forms” (Madrid: Biblioteca de la Revista Matemática Iberoamericana 1995) by the same author, which was reviewed in Zbl 0847.11028. The text of this new edition agrees with that of the first edition up to a few minor revisions, additions, rearrangements and updates. So the review of the first edition applies unchanged to the new one.
The book gives a superb introduction to real analytic automorphic forms and their applications in number theory starting at a modest level and leading up to topics of current research. Clearly this book belongs in any institutional library. If you did not succeed in buying your copy of the first edition hurry up and order your copy of this new one.
The book gives a superb introduction to real analytic automorphic forms and their applications in number theory starting at a modest level and leading up to topics of current research. Clearly this book belongs in any institutional library. If you did not succeed in buying your copy of the first edition hurry up and order your copy of this new one.
Reviewer: Jürgen Elstrodt (Münster)
MSC:
| 11F72 | Spectral theory; trace formulas (e.g., that of Selberg) |
| 11F12 | Automorphic forms, one variable |
| 11F30 | Fourier coefficients of automorphic forms |
| 11-02 | Research exposition (monographs, survey articles) pertaining to number theory |
| 11M36 | Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) |
| 58J50 | Spectral problems; spectral geometry; scattering theory on manifolds |
| 35P10 | Completeness of eigenfunctions and eigenfunction expansions in context of PDEs |
| 11L05 | Gauss and Kloosterman sums; generalizations |
| 35P20 | Asymptotic distributions of eigenvalues in context of PDEs |
| 11F66 | Langlands \(L\)-functions; one variable Dirichlet series and functional equations |
