By Joseph Bernstein, Stephen Gelbart, S.S. Kudla, E. Kowalski, E. de Shalit, D. Gaitsgory, J.W. Cogdell, D. Bump
For the earlier numerous a long time the speculation of automorphic types has turn into an important point of interest of improvement in quantity concept and algebraic geometry, with purposes in lots of different components, together with combinatorics and mathematical physics.
The twelve chapters of this monograph current a vast, basic advent to the Langlands application, that's, the speculation of automorphic kinds and its reference to the idea of L-functions and different fields of arithmetic.
Key positive factors of this self-contained presentation:
numerous components in quantity idea from the classical zeta functionality as much as the Langlands application are coated.
The exposition is systematic, with each one bankruptcy concentrating on a selected subject dedicated to specified circumstances of this system:
• simple zeta functionality of Riemann and its generalizations to Dirichlet and Hecke L-functions, type box conception and a few subject matters on classical automorphic functions (E. Kowalski)
• A learn of the conjectures of Artin and Shimura–Taniyama–Weil (E. de Shalit)
• An exam of classical modular (automorphic) L-functions as GL(2) capabilities, bringing into play the speculation of representations (S.S. Kudla)
• Selberg's idea of the hint formulation, that's the way to examine automorphic representations (D. Bump)
• dialogue of cuspidal automorphic representations of GL(2,(A)) ends up in Langlands concept for GL(n) and the significance of the Langlands twin workforce (J.W. Cogdell)
• An advent to the geometric Langlands application, a brand new and energetic sector of study that enables utilizing robust tools of algebraic geometry to build automorphic sheaves (D. Gaitsgory)
Graduate scholars and researchers will take advantage of this gorgeous text.