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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

Dieter Klusch (1991)

Acta Arithmetica

On Galois representations defined by torsion points of modular elliptic curves

P. Bayer, J. C. Lario (1992)

Compositio Mathematica

On Hecke L-functions associated with cusp forms

A. Sankaranarayanan (2003)

Acta Arithmetica

On higher moments of Hecke eigenvalues attached to cusp forms

Guodong Hua (2022)

Czechoslovak Mathematical Journal

Let $f$ , $g$ and $h$ be three distinct primitive holomorphic cusp forms of even integral weights $k_{1}$ , $k_{2}$ and $k_{3}$ for the full modular group $Γ = SL (2, ℤ)$ , respectively, and let $λ_{f} (n)$ , $λ_{g} (n)$ and $λ_{h} (n)$ denote the $n$ th normalized Fourier coefficients of $f$ , $g$ and $h$ , respectively. We consider the cancellations of sums related to arithmetic functions $λ_{g} (n)$ , $λ_{h} (n)$ twisted by $λ_{f} (n)$ and establish the following results: $\sum_{n \leq x} λ_{f} (n) λ_{g} {(n)}^{i} λ_{h} {(n)}^{j} ≪_{f, g, h, ε} x^{1 - 1 / 2^{i + j} + ε}$ for any $ε > 0$ , where $1 \leq i \leq 2$ , $j \geq 5$ are any fixed positive integers.

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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 $Λ$ -adic forms

On Cusp Forms in Character Varieties.

On effective determination of symmetric-square lifts

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

On Modular Forms whose Fourier Coefficients are Non-Negative Integers with the Constant Term Unity.

On $p$ -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

On Ramanujan's cubic continued fraction

Currently displaying 161 – 180 of 369