The Central value of the Rankin–Selberg L-Functions

By Xiaoqing Li. 2008

86 citations recorded by the source corpus.

Abstract.Let f be a Maass form for SL$$(3, {\mathbb{Z}})$$ which is fixed and uj be an orthonormal basis of even Maass forms for SL$$(2, {\mathbb{Z}})$$, we prove an asymptotic formula for the average of the product of the Rankin–Selberg L-function of f and uj and the L-function of uj at the central value 1/2. This implies simultaneous nonvanishing results of these L-functions at 1/2.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8b7ae570f9eeaca2a75ad86c10fdb2a6a33e2b95

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Subconvexity for twisted L-functions on GL(3) (2012, background): “This is given in [Li1, Lemma 6.1], but we need a slightly more precise version that is sign sensitive: L EMMA 6.”
The Second Moment of Twisted Modular L-Functions (2014, methodology): “error terms in the case r = 4 have been established by Kowalski-Michel-VanderKam [KMV], Iwaniec-Sarnak [IS], Blomer [Bl2], and with a slightly broader interpretation of the notion of a “moment” by Li [Li] and Khan [Kh]. 2010 Mathematics Subject Classiﬁcation. Primary 11F66; Secondary 11L07, 11F72. K”
Twisted moments of L-functions and spectral reciprocity (2017, background): “n procedure possible, which seems to be hard to implement in the work of [KY]. The idea of coupling a 4 = 3 + 1 structure along with arithmetic reciprocity (1.15) goes back to important work of X. Li [Li1] and was ﬁrst used for varying levels by the second author in [Kh]. 1.4. A roadmap. Sections 2 ”
On the Voronoĭ formula for GL(n) (2013, methodology): “Recent applications of the formula for GL(3) may be found in Miller-Schmid [28, 30], Sarnak-Watson [32] and Li [26, 27].”