The construction of modular forms as products of transforms of the Dedekind eta function
The covolume of quaternion groups on the four-dimensional hyperbolic space
The critical order of vanishing of automorphic L-functions with large level.
The critical values of certain Dirichlet series.
The cubic moment of central values of automorphic -functions.
The decomposition of
The determination of parabolic points in modular and extended modular groups by continued fractions.
The Dimension of the Spaces of Cusp Forms on Siegel Upper Half Plane of Degree Two.
The Dirichlet series of Koecher and Maaß and modular forms of weight 3/2.
The distribution of Fourier coefficients of cusp forms over sparse sequences
Let be the nth normalized Fourier coefficient of a holomorphic Hecke eigenform . We establish that for j = 2,3,4, which improves the previous results. For j = 2, we even establish a better result.
The distribution of the eigenvalues of Hecke operators
The Doi-Naganuma Lifting of Quaternary Theta Series.
The Drinfeld Modular Jacobian has connected fibers
We study the integral model of the Drinfeld modular curve for a prime . A function field analogue of the theory of Igusa curves is introduced to describe its reduction mod . A result describing the universal deformation ring of a pair consisting of a supersingular Drinfeld module and a point of order in terms of the Hasse invariant of that Drinfeld module is proved. We then apply Jung-Hirzebruch resolution for arithmetic surfaces to produce a regular model of which, after contractions in...
The Ehrhart polynomial of a lattice -simplex.
The Eichler Cohomology of a Kleinian Group.
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 Eisenstein descent on J0 (N).
The Eisenstein family for the modular group along closed geodescis.
The Equations Defining Abelian Varieties and Modular Functions.
The Equations for Modular Function Fields of Principal congruence subgroups of prime level.