Rankin–Selberg L-functions and “beyond endoscopy”
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-019-02431-5
Abstract: Let f and g be two holomorphic cuspidal Hecke eigenforms on the full modular group $$ \text {SL}_{2}({\mathbb {Z}}). $$ We show that the Rankin–Selberg L-function $$L(s, f \times g)$$ has no pole at $$s=1$$… read more here.
Keywords: functions beyond; beyond endoscopy; vert; selberg functions ... See more keywords
On the Beilinson–Bloch–Kato conjecture for Rankin–Selberg motives
Sign Up to like & getrecommendations! Published in 2022 at "Inventiones mathematicae"
DOI: 10.1007/s00222-021-01088-4
Abstract: In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that if the central critical value… read more here.
Keywords: conjecture; rankin selberg; bloch kato; kato ... See more keywords
Rankin–Selberg periods for spherical principal series
Sign Up to like & getrecommendations! Published in 2021 at "manuscripta mathematica"
DOI: 10.1007/s00229-021-01295-6
Abstract: By the unfolding method, Rankin-Selberg L-functions for ${\rm GL}(n)\times{\rm GL}(m)$ can be expressed in terms of period integrals. These period integrals actually define invariant forms on tensor products of the relevant automorphic representations. By the… read more here.
Keywords: rankin selberg; spherical principal; principal series; invariant forms ... See more keywords
Hybrid bounds for Rankin–Selberg L-functions
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2016.11.009
Abstract: Abstract Let M be a square-free integer and P be a prime such that ( P , M ) = 1 . We prove a new hybrid bound for L ( 1 2 , f… read more here.
Keywords: selberg functions; hybrid bounds; rankin selberg; bounds rankin ... See more keywords
TEST VECTORS FOR LOCAL CUSPIDAL RANKIN–SELBERG INTEGRALS
Sign Up to like & getrecommendations! Published in 2017 at "Nagoya Mathematical Journal"
DOI: 10.1017/nmj.2017.32
Abstract: Let $\unicode[STIX]{x1D70B}_{1},\unicode[STIX]{x1D70B}_{2}$ be a pair of cuspidal complex, or $\ell$ -adic, representations of the general linear group of rank $n$ over a nonarchimedean local field $F$ of residual characteristic $p$ , different to $\ell$ .… read more here.
Keywords: cuspidal; unicode stix; rankin selberg; stix x1d70b ... See more keywords
Local Rankin–Selberg integrals for Speh representations
Sign Up to like & getrecommendations! Published in 2020 at "Compositio Mathematica"
DOI: 10.1112/s0010437x2000706x
Abstract: We construct analogues of Rankin–Selberg integrals for Speh representations of the general linear group over a $p$-adic field. The integrals are in terms of the (extended) Shalika model and are expected to be the local… read more here.
Keywords: rankin selberg; local rankin; model; selberg integrals ... See more keywords
LEVEL RECIPROCITY IN THE TWISTED SECOND MOMENT OF RANKIN–SELBERG $L$ -FUNCTIONS
Sign Up to like & getrecommendations! Published in 2018 at "Mathematika"
DOI: 10.1112/s0025579318000256
Abstract: We prove an exact formula for the second moment of Rankin–Selberg $L$ -functions $L(\frac{1}{2},f\times g)$ twisted by $\unicode[STIX]{x1D706}_{f}(p)$ , where $g$ is a fixed holomorphic cusp form and $f$ is summed over automorphic forms of… read more here.
Keywords: rankin selberg; selberg functions; moment rankin; second moment ... See more keywords
Stability of Rankin–Selberg gamma factors for Sp(2n),Sp̃(2n) and U(n,n)
Sign Up to like & getrecommendations! Published in 2017 at "International Journal of Number Theory"
DOI: 10.1142/s1793042117501317
Abstract: Let F be a p-adic field and E/F be a quadratic extension. In this paper, we prove a stability result on partial Bessel functions associated with Howe vectors for generic representations of reductiv... read more here.
Keywords: selberg gamma; stability rankin; gamma factors; rankin selberg ... See more keywords
Rankin–Selberg L-functions via good sections
Sign Up to like & getrecommendations! Published in 2020 at "Forum Mathematicum"
DOI: 10.1515/forum-2019-0207
Abstract: Abstract In this article, we revisit Rankin–Selberg integrals established by Jacquet, Piatetski-Shapiro and Shalika. We prove the equality of Rankin–Selberg local factors defined with Schwartz–Bruhat functions and the factors attached to good sections, introduced by… read more here.
Keywords: good sections; selberg functions; exceptional poles; rankin selberg ... See more keywords
A Note on p-adic Rankin–Selberg L-functions
Sign Up to like & getrecommendations! Published in 2018 at "Canadian Mathematical Bulletin"
DOI: 10.4153/cmb-2017-047-9
Abstract: Abstract We prove an interpolation formula for the values of certain $p$ -adic Rankin-Selberg $L$ -functions associated with non-ordinary modular forms. read more here.
Keywords: note adic; adic rankin; selberg functions; rankin selberg ... See more keywords