* uschian groups of the first kind * Automorphic forms and functions * Hecke operators and the zeta-functions associated with modular forms * Elliptic curves * Abelian extensions of imaginary quadratic fields and complex multiplication of elliptic curves * Modular functions of higher level * Zeta-functions of algebraic curves and abelian varieties * The cohomology group assoicated with cusp forms * Arithmetic Fuschian groups

Introduction to the arithmetic theory of automorphic functions

Determine the value of the variable in each equation.

Basic Algebra = 代数学入門

We consider several questions about restriction of representations of classical and metaplectic groups over local and global fields to subgroups, extending considerably the scope of the earlier work on $SO(n),SO(n-1)$. This includes Bessel and Fourier-Jacobi models too. We formulate several conjectures about these restriction problems involving root numbers of symplectic representations in the local case, and central critical L-value in the global case. Along the way we prove several results both in number theory and representation theory.

Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups

In the local, characteristic 0, non-Archimedean case, we consider distributions on GL(n + 1) which are invariant under the adjoint action of GL(n). We prove that such distributions are invariant by transposition. This implies multiplicity at most one for restrictions from GL(n + 1) to GL(n). Similar theorems are obtained for orthogonal or unitary groups.

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Multiplicity one theorems

Introduction Statement of the main theorems Local character identities and the intertwining relation Trace formulas and their stabilization The Standard model Study of critical cases Local classification Nontempered representations Global classification Addendum Bibliography

Endoscopic Classification of Representations of Quasi-split Unitary Groups

We prove the local Langlands conjecture for GSp4(F ) where F is a nonarchimedean local eld of characteristic zero.

http://annals.math.princeton.edu/wp-content/uploads/annals-v173-n3-p12-p.pdf

The local Langlands conjecture for GSp(4)

We prove the local Langlands conjecture for $GSp_4(F)$ where $F$ is a non-archimedean local field of characteristic zero.

The Local Langlands Conjecture for GSp(4)

Using theta correspondence, we classify the irreducible representations of Mp2n in terms of the irreducible representations of SO2n+1 and determine many properties of this classification. This is a local Shimura correspondence which extends the well-known results of Waldspurger for n=1.

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Representations of metaplectic groups I: epsilon dichotomy and local Langlands correspondence

We develop a theory of Fourier coefficients for modular forms on the split exceptional group G2 over ℚ.

Wee Teck Gan

Papers

Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups

The local Langlands conjecture for GSp(4)

The Local Langlands Conjecture for GSp(4)

Representations of metaplectic groups I: epsilon dichotomy and local Langlands correspondence

Fourier coefficients of modular forms on G2