On a short spectral sum involving inner products of a holomorphic cusp form and Maass forms
Eeva Suvitie (2010)
Acta Arithmetica
Tomoyoshi Ibukiyama, Yasutaka Ihara (1987)
Mathematische Annalen
Tsuneo Ishikawa (2003)
Acta Arithmetica
Masao Toyoizumi (1988)
Acta Arithmetica
Ian Kiming (1995)
Manuscripta mathematica
Haruzo Hida (1981)
Inventiones mathematicae
Fred Diamond (1989)
Compositio Mathematica
P. Sarnak, R. Philips (1994)
Geometric and functional analysis
Qingfeng Sun (2014)
Open Mathematics
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.
Dieter Klusch (1991)
Acta Arithmetica
P. Bayer, J. C. Lario (1992)
Compositio Mathematica
A. Sankaranarayanan (2003)
Acta Arithmetica
Guodong Hua (2022)
Czechoslovak Mathematical Journal
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.
Michio Ozeki (1973)
Mathematische Annalen
B. Mazur, A. Wiles (1986)
Compositio Mathematica
Marvin Knopp (1986)
Acta Arithmetica
Eknath Ghate (2002)
Acta Arithmetica
W. Kohnen, J. Sengupta (2001)
Acta Arithmetica
P. Guerzhoy (1997)
Acta Arithmetica
Heng Huat Chan (1995)
Acta Arithmetica