Odd values of the Ramanujan -function
On a short spectral sum involving inner products of a holomorphic cusp form and Maass forms
On Automorphic Forms on the Unitary Symplectic Group Sp (n) and SL2 (R).
On certain congruences for Fourier coefficients of classical cusp forms
On certain infinite products III
On certain problems in the analytical arithmetic of quadratic forms arising from the theory of curves of genus 2 with elliptic differentials.
On Congruence Divisors of Cusp Forms as Factors of Special Values of Their Zeta Functions.
On congruence modules associated to -adic forms
On Cusp Forms in Character Varieties.
On effective determination of symmetric-square lifts
Let F be the symmetric-square lift with Laplace eigenvalue λ F (Δ) = 1+4µ2. Suppose that |µ| ≤ Λ. We show that F is uniquely determined by the central values of Rankin-Selberg L-functions L(s, F ⋇ h), where h runs over the set of holomorphic Hecke eigen cusp forms of weight κ ≡ 0 (mod 4) with κ≍ϱ+ɛ, t9 = max {4(1+4θ)/(1−18θ), 8(2−9θ)/3(1−18θ)} for any 0 ≤ θ < 1/18 and any ∈ > 0. Here θ is the exponent towards the Ramanujan conjecture for GL2 Maass forms.
On entry 8 of Chapter 15 of Ramanujan's Notebook II
On Galois representations defined by torsion points of modular elliptic curves
On Hecke L-functions associated with cusp forms
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 Modular Forms whose Fourier Coefficients are Non-Negative Integers with the Constant Term Unity.
On -adic analytic families of Galois representations
On powers of the theta-function greater than the eighth
On products of eigenforms
On quadratic character twists of Hecke L-functions attached to cusp forms of varying weights at the central point
On Ramanujan congruences between special values of Hecke and Dirichlet L-functions