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We give a simple proof that critical values of any Artin $L$ -function attached to a representation $ρ$ with character $χ_{ρ}$ are stable under twisting by a totally even character $χ$ , up to the $dim ρ$ -th power of the Gauss sum related to $χ$ and an element in the field generated by the values of $χ_{ρ}$ and $χ$ over $ℚ$ . This extends a result of Coates and Lichtenbaum as well as the previous work of Ward.

On determination of GL₃ cusp forms

Qingfeng Sun (2012)

Acta Arithmetica

On Dirichlet series associated with cubic Gauss sums.

S.J. Patterson (1978)

Journal für die reine und angewandte Mathematik

On distinguished representations.

Yuval Z. Flicker (1991)

Journal für die reine und angewandte Mathematik

On effective determination of symmetric-square lifts

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.

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On a short spectral sum involving inner products of a holomorphic cusp form and Maass forms

On a theorem of Waldspurger and on Eisenstein series of Klingen type.

On arithmetic quotients of the Siegel upper half space of degree two

On Automorphic Forms and Hodge Theory.

On Automorphic Forms on the Unitary Symplectic Group Sp (n) and SL2 (R).

On Certain Dirichlet Series Associated with Automorphic Forms on SL (2, C).

On certain Euler products for SU $(2, 1)$

On certain Galois representations related to the modular curve $X_{1} (p)$

On certain infinite products III

On Congruence Divisors of Cusp Forms as Factors of Special Values of Their Zeta Functions.

On critical values of twisted Artin $L$ -functions

On determination of GL₃ cusp forms

On Dirichlet series associated with cubic Gauss sums.

On distinguished representations.

On effective determination of symmetric-square lifts

On Eisenstein series with characters and Dedekind sums

On Euler products and residual Eisenstein cohomology classes for Siegel modular varieties.

On Hsiao's conjecture on Hecke groups.

On Integrality of Certain Algebraic Numbers Associated with Modular Forms.

On L-functions for GSp(4) X GL(2) and their special values.

Currently displaying 1 – 20 of 47