On the fundamental periods of automorphic forms of arithmetic type.
On the Holomorphic Differential Forms of the Siegel Modular Variety II.
On the Shimura correspondence for GSp(4).
On the spezialschar of Maass.
-adic Differential Operators on Automorphic Forms on Unitary Groups
The goal of this paper is to study certain -adic differential operators on automorphic forms on . These operators are a generalization to the higher-dimensional, vector-valued situation of the -adic differential operators constructed for Hilbert modular forms by N. Katz. They are a generalization to the -adic case of the -differential operators first studied by H. Maass and later studied extensively by M. Harris and G. Shimura. The operators should be useful in the construction of certain -adic...
Quadratic polynomials, period polynomials, and Hecke operators
For any non-square 1 < D ≡ 0,1 (mod 4), Zagier defined . Here we use the theory of periods to give identities and congruences which relate various values of .
Shimura correspondence of Maass wave forms of half integral weight
Special values of symmetric power -functions and Hecke eigenvalues
We compute the moments of -functions of symmetric powers of modular forms at the edge of the critical strip, twisted by the central value of the -functions of modular forms. We show that, in the case of even powers, it is equivalent to twist by the value at the edge of the critical strip of the symmetric square -functions. We deduce information on the size of symmetric power -functions at the edge of the critical strip in subfamilies. In a second part, we study the distribution of small and...
The Eichler Commutation Relation for theta series with spherical harmonics
It is well known that classical theta series which are attached to positive definite rational quadratic forms yield elliptic modular forms, and linear combinations of theta series attached to lattices in a fixed genus can yield both cusp forms and Eisenstein series whose weight is one-half the rank of the quadratic form. In contrast, generalized theta series - those augmented with a spherical harmonic polynomial - will always yield cusp forms whose weight is increased by the degree of the...
The Maaß spaces on the Hermitian half-space of degree 2.
Theta correspondence and Hecke operators relative to a quadratic extension
Theta-transforms and even zeta functions of Siegel modular forms
Локальная двойственность операторов Гекке симплектической и ортогональной группы
Об одном совете Ю.В. Линника, операторах Гекке и тета-функциях
Операторы Гекке симплектической группы рода 2 над вещественным полем
Параболические расширения кольца Гекке полной линейной группы. II.
Функции Якоби и эйлеровы произведения для эрмитoвых модулярных форм