On embedding numbers into quaternion orders.
On endo-lifting
On entire modular forms of half-integral weight on the congruence subgroup .
On entry 8 of Chapter 15 of Ramanujan's Notebook II
On Euler products and residual Eisenstein cohomology classes for Siegel modular varieties.
On Even Unimodular Positive Definite Quadratic Lattices of Rank 32.
On explicit construction of Hilbert-Siegel modular forms of degree two
On explicit lifts of cusp forms from to classical groups.
On exponential sums involving the Fourier coefficients of Maass wave forms.
On families of 9-congruent elliptic curves
We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over ℚ, i.e. pairs of non-isogenous elliptic curves over ℚ whose 9-torsion subgroups are isomorphic as Galois modules.
On families of counting functions of number fields and hyperbolic manifolds of dimensions two and three
On Fourier coefficients of modular forms of different weights
On Fourier coefficients of Siegel modular forms.
On Galois representations associated to Hilbert modular forms.
On Galois representations associated to Hilbert modular forms.
On Galois representations defined by torsion points of modular elliptic curves
On general L-functions
On generalized Fermat equations of signature (p,p,3)
This paper focuses on the Diophantine equation , with fixed α, p, and M. We prove that, under certain conditions on M, this equation has no non-trivial integer solutions if , where is an effective constant. This generalizes Theorem 1.4 of the paper by Bennett, Vatsal and Yazdani [Compos. Math. 140 (2004), 1399-1416].
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)].