A conjecture on Whittaker–Fourier coefficients of cusp forms

Lapid, Erez; Mao, Zhengyu

doi:10.1016/j.jnt.2013.10.003

Cited by 61 publications

(69 citation statements)

References 73 publications

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“…In particular, when G 0 is the trivial group, the terms L. 1 2 ; 2 0 / and L.1; 0 ; Ad/ are both 1, then the refined formula computes the (square norm of the) Whittaker-Fourier coefficient. In this case, the refined formula has also been conjectured by Lapid-Mao [33] for more general groups; see Section 2.2 for details. The extra constant term 1=jS ‰ j relates to the Arthur parameter ‰ of 2 0 , which was first observed by Ichino-Ikeda after summarizing many low-rank examples in the case r D 0.…”

supporting

confidence: 55%

Refined global Gan–Gross–Prasad conjecture for Bessel periods

Liu

2014

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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supporting

confidence: 55%

Refined global Gan–Gross–Prasad conjecture for Bessel periods

Liu

2014

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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“…where ∆ G,S = w∈S ∆ G,w . It is well known that this integral converges and defines a G( [LM15,p. 477] which is of course based on [JS81]) provided that S is a finite set of places of E containing all the archimedean ones as well as all the non-archimedean places for which either ϕ or ϕ ∨ is not…”

Section: The Whittaker Realization Of the Petersson Inner Product Gimentioning

confidence: 98%

Whittaker rational structures and special values of the Asai 𝐿-function

Grobner¹,

Harris²,

Lapid³

2016

Contemporary Mathematics

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Let F be a totally real number field and E/F a totally imaginary quadratic extension of F . Let Π be a cohomological, conjugate self-dual cuspidal automorphic representation of GL n (A E ). Under a certain non-vanishing condition we relate the residue and the value of the Asai L-functions at s = 1 with rational structures obtained from the cohomologies in top and bottom degrees via the Whittaker coefficient map. This generalizes a result in Eric Urban's thesis when n = 2, as well as a result of the first two named authors, both in the case F = Q.

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“…Suppose that F is a non-archimedean local field. We consider the notion of a stable integral as defined in [13]. We refer the reader to there for more information since it is not of central importance to our discussion.…”

Section: Local Integralsmentioning

confidence: 99%

A proof of the refined Gan–Gross–Prasad conjecture for non-endoscopic Yoshida lifts

Corbett

2016

Forum Mathematicum

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Abstract. We prove a precise formula relating the Bessel period of certain automorphic forms on GSp 4 (AF ) to a central L-value. This is a special case of the refined Gan-Gross-Prasad conjecture for the groups (SO5, SO2) as set out by Ichino-Ikeda [12] and Liu [14]. This conjecture is deep and hard to prove in full generality; in this paper we succeed in proving the conjecture for forms lifted, via automorphic induction, from GL2(AE) where E is a quadratic extension of F . The case where E = F × F has been previously dealt with by Liu [14].

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A conjecture on Whittaker–Fourier coefficients of cusp forms

Abstract: Abstract. We formulate an analogue of the Ichino-Ikeda conjectures for the WhittakerFourier coefficients of automorphic forms on quasi-split reductive groups. This sharpens the conjectures of Sakellaridis-Venkatesh in the case at hand.

Cited by 61 publications

References 73 publications

Refined global Gan–Gross–Prasad conjecture for Bessel periods

Refined global Gan–Gross–Prasad conjecture for Bessel periods

Whittaker rational structures and special values of the Asai 𝐿-function

A proof of the refined Gan–Gross–Prasad conjecture for non-endoscopic Yoshida lifts

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