Eisenstein series on reductive symmetric spaces and representations of Hecke algebras.
Eisensteinreihen für einige arithmetisch definierte Untergruppen von SL2 (IH).
Exceptional modular form of weight 4 on an exceptional domain contained in C27.
Resnikoff [12] proved that weights of a non trivial singular modular form should be integral multiples of 1/2, 1, 2, 4 for the Siegel, Hermitian, quaternion and exceptional cases, respectively. The θ-functions in the Siegel, Hermitian and quaternion cases provide examples of singular modular forms (Krieg [10]). Shimura [15] obtained a modular form of half-integral weight by analytically continuing an Eisenstein series. Bump and Bailey suggested the possibility of applying an analogue of Shimura's...
Explicit formulas for the Fourier coefficients of Jacobi and elliptic modular forms.
Extended automorphic forms on the upper half plane.
Formes automorphes et produits eulériens
Heegner cycles, modular forms and jacobi forms
We give a geometric interpretation of an arithmetic rule to generate explicit formulas for the Fourier coefficients of elliptic modular forms and their associated Jacobi forms. We discuss applications of these formulas and derive as an example a criterion similar to Tunnel's criterion for a number to be a congruent number.
Higher order invariants in the case of compact quotients
We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case, many things simplify and we are thus able to prove a more precise structure theorem than in the general case.
Hirzebruch-Mumford proportionality and locally symmetric varieties of orthogonal type.
Intersections of higher weight cycles and modular forms
Jacobi Forms and Discrete Series Representations of the Jacobi Group.
Jacobi-Eisenstein series and -adic interpolation of symmetric squares of cusp forms
The aim of this paper is to construct and calculate generating functions connected with special values of symmetric squares of modular forms. The Main Theorem establishes these generating functions to be Jacobi-Eisenstein series i.e. Eisenstein series among Jacobi forms. A theorem on -adic interpolation of the special values of the symmetric square of a -ordinary modular form is proved as a corollary of our Main Theorem.
Jacobi-Eisenstein series of degree two over Cayley numbers.
We shall develop the general theory of Jacobi forms of degree two over Cayley numbers and then construct a family of Jacobi- Eisenstein series which forms the orthogonal complement of the vector space of Jacobi cusp forms of degree two over Cayley numbers. The construction is based on a group representation arising from the transformation formula of a set of theta series.
Kloosterman sums for Clifford algebras and a lower bound for the positive eigenvalues of the Laplacian for congruence subgroups acting on hyperbolic spaces.
l-adic representations associated to modular forms over imaginary quadratic fields. II.
L’azione del gruppo simplettico associata ad un’estensione quadratica di campi
Local Borcherds products
The local Picard group at a generic point of the one-dimensional Baily-Borel boundary of a Hermitean symmetric quotient of type is computed. The main ingredient is a local version of Borcherds’ automorphic products. The local obstructions for a Heegner divisor to be principal are given by certain theta series with harmonic coefficients. Sometimes they generate Borcherds’ space of global obstructions. In these particular cases we obtain a simple proof of a result due to the first author: Suppose...
Mellin transforms of Whittaker functions on GL(4, R) and GL(4, C).
Mémoire de Langlands sur la dimension des espaces de formes automorphes
Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey)
Modular invariance property of association schemes is recalled in connection with our joint work with François Jaeger. Then we survey codes over discussing how codes, through their (various kinds of) weight enumerators, are related to (various kinds of) modular forms through polynomial invariants of certain finite group actions and theta series. Recently, not only codes over an arbitrary finite field but also codes over finite rings and finite abelian groups are considered and have been studied...