# Contributions to Automorphic Forms, Geometry, and Number by Haruzo Hida, Dinakar Ramakrishnan, Freydoon Shahidi

By Haruzo Hida, Dinakar Ramakrishnan, Freydoon Shahidi

In *Contributions to Automorphic kinds, Geometry, and quantity Theory*, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi compile a uncommon team of specialists to discover automorphic varieties, largely through the linked L-functions, illustration thought, and geometry. simply because those topics are on the innovative of a vital quarter of contemporary arithmetic, and are regarding the philosophical base of Wiles' facts of Fermat's final theorem, this booklet could be of curiosity to operating mathematicians and scholars alike. by no means formerly released, the contributions to this quantity reveal the reader to a number of tricky and thought-provoking difficulties.

Each of the intense and remarkable mathematicians during this quantity makes a special contribution to a box that's presently seeing explosive development. New and robust effects are being proved, considerably and consistently altering the field's make up. *Contributions to Automorphic types, Geometry, and quantity Theory* will most likely result in very important interplay between researchers and likewise support arrange scholars and different younger mathematicians to go into this fascinating zone of natural arithmetic.

Contributors: Jeffrey Adams, Jeffrey D. Adler, James Arthur, Don Blasius, Siegfried Boecherer, Daniel Bump, William Casselmann, Laurent Clozel, James Cogdell, Laurence Corwin, Solomon Friedberg, Masaaki Furusawa, Benedict Gross, Thomas Hales, Joseph Harris, Michael Harris, Jeffrey Hoffstein, Hervé Jacquet, Dihua Jiang, Nicholas Katz, Henry Kim, Victor Kreiman, Stephen Kudla, Philip Kutzko, V. Lakshmibai, Robert Langlands, Erez Lapid, Ilya Piatetski-Shapiro, Dipendra Prasad, Stephen Rallis, Dinakar Ramakrishnan, Paul Sally, Freydoon Shahidi, Peter Sarnak, Rainer Schulze-Pillot, Joseph Shalika, David Soudry, Ramin Takloo-Bigash, Yuri Tschinkel, Emmanuel Ullmo, Marie-France Vignéras, Jean-Loup Waldspurger.

**Read or Download Contributions to Automorphic Forms, Geometry, and Number Theory: A Volume in Honor of Joseph Shalika PDF**

**Best number theory books**

**Multiplicative Number Theory I. Classical Theory**

A textual content in response to classes taught effectively over decades at Michigan, Imperial collage and Pennsylvania country.

**Mathematical Problems in Elasticity**

This quantity beneficial properties the result of the authors' investigations at the improvement and alertness of numerical-analytic equipment for traditional nonlinear boundary worth difficulties (BVPs). The equipment into account provide a chance to unravel the 2 vital difficulties of the BVP conception, specifically, to set up lifestyles theorems and to construct approximation strategies

**Iwasawa Theory Elliptic Curves with Complex Multiplication: P-Adic L Functions**

Within the final fifteen years the Iwasawa thought has been utilized with notable luck to elliptic curves with advanced multiplication. a transparent but normal exposition of this concept is gifted during this book.

Following a bankruptcy on formal teams and native devices, the p-adic L services of Manin-Vishik and Katz are developed and studied. within the 3rd bankruptcy their relation to classification box conception is mentioned, and the purposes to the conjecture of Birch and Swinnerton-Dyer are handled in bankruptcy four. complete proofs of 2 theorems of Coates-Wiles and of Greenberg also are awarded during this bankruptcy that could, furthermore, be used as an creation to the more moderen paintings of Rubin.

The publication is basically self-contained and assumes familiarity simply with basic fabric from algebraic quantity conception and the idea of elliptic curves. a few effects are new and others are provided with new proofs.

- First course in theory of numbers
- Algebraic Number Theory (Springer Undergraduate Mathematics Series)
- Number Theory and its Applications
- Mathematical Mysteries: The Beauty and Magic of Numbers
- The Fourier-Analytic Proof of Quadratic Reciprocity
- Einführung in Algebra und Zahlentheorie

**Extra resources for Contributions to Automorphic Forms, Geometry, and Number Theory: A Volume in Honor of Joseph Shalika**

**Example text**

Let V be a four-dimensional real vector space with a non-degenerate symplectic form < , >. Let G = Sp(V ) = Sp(V , < , >) be the isometry group of < , >. Choose a basis of V such that < , > is given by J = ( −I0 2 I02 ). Then Sp(V ) is isomorphic to G = Sp(4, R), the group of matrices g satisfying g J tg = J . Thus B ) where G consists of the matrices ( CA D A tB = t( A tB) C tD = t(C tD) A tD − B tC = I2 . Let g0 be the Lie algebra of G. , X = ( CA −BtA ) where B and C are symmetric. We will make repeated use of the Cartan subgroups of G.

3 we have Nk (ηx ) = TX˜ ,n Nk . This completes the result for even n. For n odd, n = 2k + 1 we may write n ∈ Nk+1 uniquely in the form n = 1 + π k+1 (again, is taken mod pk ), Tr( ) ≡ 0 mod pk . As before, Nk+1 , gk and g∗k are isomorphic as K n -modules. In this case however for x ∈ gk , x primitive, X a pre-image in g, Nk+1 (ηx ) = TX˜ ,n Nk . 0 ∗ ), where λ ∈ Op , In what follows X will denote an element of g of the form ( λ0 −λ 0 ζ ∗ or one of the form ( ω˜ 0 ), where ζ ∈ Op and ω ˜ ∈ p. In particular X is primitive.

H. Rohrbach, Die character der bin¨aren konguence gruppen mod p 2 , Schriften d. math. Seminars d. Univ. Berlin 1 (1932), 33–94. J. Schur, Undtersuchungen u¨ ber die darstellung der endlichen gruppen durch gebrochene lineare substitution, J. Reine Angew. Math. 132 (1907), 85–137. H. Spies, Die darstellung der inhomogen modulargruppen mod q n durch die ganzen modulformen gerader dimension, Math. Ann. 111 (1935), 329–354. A. Weil, Sur certains groupes d’op´erateurs unitaires, Acta Math. 111 (1964), 143–211.