scholarly journals Determination of GL(3) Hecke–Maass forms from twisted central values

2015 ◽  
Vol 148 ◽  
pp. 272-287 ◽  
Author(s):  
Ritabrata Munshi ◽  
Jyoti Sengupta
Keyword(s):  
Maass Forms ◽  
Central Values

On effective determination of symmetric-square lifts

2014 ◽  
Vol 12 (7) ◽  
Author(s):  
Qingfeng Sun
Keyword(s):  
Cusp Forms ◽  
Maass Forms ◽  
Central Values ◽  
Laplace Eigenvalue ◽  
Symmetric Square ◽  
Ramanujan Conjecture

AbstractLet 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.

scholarly journals On effective determination of Maass forms from central values of Rankin–Selberg L-function

2015 ◽  
Vol 27 (1) ◽  
Author(s):  
Ritabrata Munshi ◽  
Jyoti Sengupta
Keyword(s):  
Cusp Form ◽  
Maass Forms ◽  
Central Values ◽  
Maass Cusp Form

AbstractWe address the problem of identifying a Hecke–Maass cusp form

On effective determination of symmetric-square lifts, level aspect

2014 ◽  
Vol 11 (01) ◽  
pp. 51-65
Author(s):  
Qingfeng Sun
Keyword(s):  
Cusp Forms ◽  
Maass Forms ◽  
Central Values ◽  
Laplace Eigenvalue ◽  
Holomorphic Cusp Forms ◽  
Symmetric Square ◽  
Ramanujan Conjecture ◽  
Level Aspect

Let F be the symmetric-square lift with Laplace eigenvalue λF(Δ) = 1 + 4μ2. Suppose that |μ| ≤ Λ. It is proved 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 cusp forms of weight 10 and level q ≈ Λϱ+ϵ with [Formula: see text] for any ϵ > 0. Here θ is the exponent towards the Ramanujan conjecture for GL2 Maass forms. We also prove an unconditional result in weight aspect.

scholarly journals EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES

2020 ◽  
pp. 1-36
Author(s):  
Bart Michels
Keyword(s):  
Lower Bound ◽  
Closed Geodesic ◽  
Extreme Values ◽  
Theta Series ◽  
Hyperbolic Surface ◽  
Quadratic Fields ◽  
Maass Forms ◽  
Real Quadratic Fields ◽  
Central Values ◽  
Real Quadratic

Abstract Given a closed geodesic on a compact arithmetic hyperbolic surface, we show the existence of a sequence of Laplacian eigenfunctions whose integrals along the geodesic exhibit nontrivial growth. Via Waldspurger’s formula we deduce a lower bound for central values of Rankin-Selberg L-functions of Maass forms times theta series associated to real quadratic fields.

scholarly journals Twisted moments of GL(3) ×GL(2) L-functions

2021 ◽  
pp. 1-34
Author(s):  
Jakob Streipel
Keyword(s):  
Asymptotic Formula ◽  
Maass Forms ◽  
Central Values ◽  
Symmetric Square ◽  
Derivatives Of

We compute an asymptotic formula for the twisted moment of [Formula: see text] [Formula: see text]-functions and their derivatives. As an application, we prove that symmetric-square lifts of [Formula: see text] Maass forms are uniquely determined by the central values of the derivatives of [Formula: see text] [Formula: see text]-functions.

Determination of ${\bf GL}(2)$ Maass forms from twists in the level aspect

2019 ◽  
Vol 189 (2) ◽  
pp. 165-178
Author(s):  
Biswajyoti Saha ◽  
Jyoti Sengupta
Keyword(s):  
Maass Forms ◽  
Level Aspect

scholarly journals A first determination of parton distributions with theoretical uncertainties

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Rabah Abdul Khalek ◽  
Richard D. Ball ◽  
Stefano Carrazza ◽  
Stefano Forte ◽  
Tommaso Giani ◽  
...  
Keyword(s):  
Covariance Matrix ◽  
Hadron Collider ◽  
Distribution Functions ◽  
Leading Order ◽  
Parton Distribution Functions ◽  
Parton Distributions ◽  
Central Values ◽  
Sources Of Uncertainty ◽  
Fixed Order

Abstract The parton distribution functions (PDFs) which characterize the structure of the proton are currently one of the dominant sources of uncertainty in the predictions for most processes measured at the Large Hadron Collider (LHC). Here we present the first extraction of the proton PDFs that accounts for the missing higher order uncertainty (MHOU) in the fixed-order QCD calculations used in PDF determinations. We demonstrate that the MHOU can be included as a contribution to the covariance matrix used for the PDF fit, and then introduce prescriptions for the computation of this covariance matrix using scale variations. We validate our results at next-to-leading order (NLO) by comparison to the known next order (NNLO) corrections. We then construct variants of the NNPDF3.1 NLO PDF set that include the effect of the MHOU, and assess their impact on the central values and uncertainties of the resulting PDFs.

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