Eisenstein Series and Automorphic $L$-Functions

Freydoon Shahidi, Purdue University, West Lafayette, IN

Written by one of the main players in the game, Eisenstein Series and Automorphic L-functions is nigh on indispensable for anyone wishing to get into this beautiful and exciting part of number theory. A glance at the table of contents of Freydoon Shahidi's book shows that it is something of a pedagogical dream: it seems to cover just about everything one might want to learn about the interface between automorphic representations and L-functions - a theme of huge importance in number theory in the last 50 years. Of course, there is more to the subject than can be covered in the book's 200 pages, but Shahidi touches on a great number of critically important topics, arranges them extremely efficiently, and then expounds them brilliantly. . . . I cannot imagine a better trajectory toward learning this material than to go through the pages of Eisenstein Series and Automorphic L-functions with a lot of note paper handy and a comfortable writing pen, to follow up on Shahidi's numerous cross-references when so indicated (and to the right degree, so to speak), and of course to fill out the sketches and do the exercises that the author presents. This very beautiful mathematics is well worth the effort."" — Michael Berg, MAA Reviews

• ChaptersIntroductionChapter 1. Reductive groupsChapter 2. Satake isomorphismsChapter 3. Generic representationsChapter 4. Intertwining operatorsChapter 5. Local coefficientsChapter 6. Eisenstein seriesChapter 7. Fourier coefficients of Eisenstein seriesChapter 8. Functional equationsChapter 9. Further properties of $L$-functionsChapter 10. Applications to functorialityAppendices: Tables of Dynkin diagrams