Lectures on Automorphic $L$-functions
and M. Ram Murty James W. Cogdell, Henry H. Kim, "Lectures on Automorphic $L$-functions "
English | ISBN: 0821835165 | 2004 | 283 pages | PDF | 23 MB
English | ISBN: 0821835165 | 2004 | 283 pages | PDF | 23 MB
This book provides a comprehensive account of the crucial role automorphic $L$-functions play in number theory and in the Langlands program, especially the Langlands functoriality conjecture. There has been a recent major development in the Langlands functoriality conjecture by the use of automorphic $L$-functions, namely, by combining converse theorems of Cogdell and Piatetski-Shapiro with the Langlands-Shahidi method. This book provides a step-by-step introduction to these developments and explains how the Langlands functoriality conjecture implies solutions to several outstanding conjectures in number theory, such as the Ramanujan conjecture, Sato-Tate conjecture, and Artin's conjecture. It would be ideal for an introductory course in the Langlands program.