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Nonlinear exponential twists of the Liouville function

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Sun Q.

Open Mathematics

2011

tom 9

nr 2

328-337

Let λ(n) be the Liouville function. We find a nontrivial upper bound for the sum $$ \sum\limits_{X \leqslant n \leqslant 2X} {\lambda (n)e^{2\pi i\alpha \sqrt n } } ,0 \ne \alpha \in \mathbb{R} $$ The main tool we use is Vaughan’s identity for λ(n).

On determination of GL₃ cusp forms

100%

Sun Q.

Acta Arithmetica

2012

tom 151

nr 1

39-54

On effective determination of symmetric-square lifts

100%

Sun Q.

Open Mathematics

2014

tom 12

nr 7

976-990

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.

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2 Open Mathematics

1 Acta Arithmetica

3 Sun Q.

1 2014

1 2012

1 2011

Wyniki wyszukiwania

Nonlinear exponential twists of the Liouville function

On determination of GL₃ cusp forms

On effective determination of symmetric-square lifts