Mellin transforms of Whittaker functions on GL(4, R) and GL(4, C).
Modular parametrizations of certain elliptic curves
Kaneko and Sakai (2013) recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a particular differential equation involving modular forms and Ramanujan-Serre differential operator. In this paper, we study certain properties of the modular parametrization associated to the elliptic curves over ℚ, and as a consequence we generalize and explain some of their findings.
Modularity of an odd icosahedral representation
In this paper, we prove that the representation from in GL with image in PGL corresponding to the example in [B-K] is modular. This representation has conductor and determinant ; its modularity was not yet proved, since this representation does not satisfy the hypothesis of the theorems of [B-D-SB-T] and [Tay2].
Multiple Dirichlet series over rational function fields
Nonvanishing of Fourier coefficients of newforms in progressions
Nonvanishing of Siegel-Poincaré series II
On a divisor problem related to the Epstein zeta-function, IV
On a short spectral sum involving inner products of a holomorphic cusp form and Maass forms
On a theorem of Waldspurger and on Eisenstein series of Klingen type.
On arbitrary products of eigenforms
We characterize all the cases in which products of arbitrary numbers of nearly holomorphic eigenforms and products of arbitrary numbers of quasimodular eigenforms for the full modular group SL₂(ℤ) are again eigenforms.
On certain congruences for Fourier coefficients of classical cusp forms
On cubic symplectic metaplectic forms.
On embedding numbers into quaternion orders.
On explicit construction of Hilbert-Siegel modular forms of degree two
On Fourier coefficients of modular forms of different weights
On Hecke eigenforms of half-integral weight.
On Hecke eigenvalues at primes of the form [g(n)]
We study the average of the Fourier coefficients of a holomorphic cusp form for the full modular group at primes of the form [g(n)].
On higher moments of Hecke eigenvalues attached to cusp forms
Let , and be three distinct primitive holomorphic cusp forms of even integral weights , and for the full modular group , respectively, and let , and denote the th normalized Fourier coefficients of , and , respectively. We consider the cancellations of sums related to arithmetic functions , twisted by and establish the following results: for any , where , are any fixed positive integers.
On Integrality of Eisenstein Liftings.
On L-functions for GSp(4) X GL(2) and their special values.