Introduction to the arithmetic theory of automorphic functions djvu

The trace of modular forms and its application to number theory. We provide a generalization of an algebraic linear combination for the trace of certain elliptic modular forms, and through specializing the expression at a suitable pair consisting of an elliptic … Expand. Eichler-Shimura isomorphism and group cohomology on arithmetic groups.

The Eichler-Shimura isomorphism realizes the automorphic representation generated by an automorphic newform in certain cohomology of an arithmetic group. In this short note, we give a cohomological … Expand. CM values of automorphic Green functions on orthogonal groups over totally real fields.

Generalizing work of Gross--Zagier and Schofer on singular moduli, we study the CM values of regularized theta lifts of harmonic Whittaker forms. We compute the archimedian part of the height pairing … Expand.

The theory of theta functions for arithmetic groups that act on the Drinfeld upper half-plane is extended to allow degenerate parameters. This is used to investigate the cuspidal divisor class groups … Expand. Construction of class fields over real quadratic fields 7.

In Chapter 7, "Zeta-functions of algebraic curves and abelian varieties", the author treats the second topic mentioned above. The conjecture of Hasse and Weil is verified for the algebraic curves uniformized by modular functions.

Further, it is shown that if a cusp form of weight 2 is a common eigenfunction of the Hecke operators, then the product of several "conjugated" Dirichlet series associated with it coincides up to finitely many Euler factors with the zeta-function of a certain abelian variety which is specifically given.

As an application of this result it is shown that some arithmetic of a real quadratic fieldits units, abelian extensions, This very interesting topic has received a wide development in the deep investigations of the author, Doi, Naganuma and Miyake. Download for print-disabled. Check nearby libraries Library. Share this book Facebook. November 18, History. An edition of Introduction to the arithmetic theory of automorphic functions Written in English — pages.

Subjects Automorphic functions. Introduction to the arithmetic theory of automorphic functions , Princeton University Press. Libraries near you: WorldCat. Introduction to the arithmetic theory of automorphic functions. But, to be sure, the book is full of wonderful arguments and complete treatments of the themes indicated above. Skip to main content. Search form Search. Login Join Give Shops. Halmos - Lester R. Ford Awards Merten M. Goro Shimura. Publication Date:.