Moments of Spinor L-Functions and Symplectic Kloosterman Sums

Waibel, Fabian

doi:10.1093/qmathj/haz024

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Cited by 2 publications

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References 24 publications

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“…Using the Petersson-Kitaoka relative trace formula, local spectral equidistribution problems in the sense of Section 3.1 have been considered in [KST]. The papers [Bl5,Wa] compute mean values of spinor L-functions with applications to non-vanishing. This uses the full force of the formula.…”

Section: Other Groupsmentioning

confidence: 99%

The relative trace formula in analytic number theory

Blomer¹

2019

Preprint

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Section: Other Groupsmentioning

confidence: 99%

The relative trace formula in analytic number theory

Blomer¹

2019

Preprint

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“…The formula (1.8.2) and its generalization (8.3.1) are expected to have a broad spectrum of interesting applications both arithmetic and analytic. Some of the examples are [10], [18, Section 3], [19], [51], [86] and [100].…”

mentioning

confidence: 99%

On the Gross-Prasad conjecture with its refinement for $\left(\mathrm{SO}\left(5\right),\mathrm{SO}\left(2\right)\right)$ and the generalized Böcherer conjecture

Furusawa¹,

Morimoto²

2022

Preprint

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A. We investigate the Gross-Prasad conjecture and its refinement for the Bessel periods in the case of (SO (5), SO(2)). In particular, by combining several theta correspondences, we prove the Ichino-Ikeda type formula for any tempered irreducible cuspidal automorphic representations. As a corollary of our formula, we prove an explicit formula relating certain weighted averages of Fourier coefficients of holomorphic Siegel cusp forms of degree two which are Hecke eigenforms to central special values of -functions. The formula is regarded as a natural generalization of Böcherer's conjecture to the non-trivial toroidal character case.1.2. Measures. Throughout the paper, for an algebraic group G defined over , we write G for G ( ) and we always take the measure on G (A) to be the Tamagawa measure unless specified otherwise. For each , we take the self-dual measure with respect to on . Then recall that the product measure on A is the self-dual measure with respect to and is also the Tamagawa measure since Vol (A/ ) = 1. For a unipotent algebraic group U defined over , we also specify the local measure on U( ) to be the measure corresponding to the gauge form defined over , together with our choice of the measure on , at each place of . Thus in particular we have = and Vol (U ( ) \U (A) , ) = 1.1.3. Similitudes. Various similitude groups appear in this article. Unless there exists a fear of confusion, we denote by ( ) the similitude of an element of a similitude group for simplicity.

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Moments of Spinor L-Functions and Symplectic Kloosterman Sums

Abstract: We compute the second moment of spinor L-functions at central points of Siegel modular forms on congruence subgroups of large prime level N and give applications to non-vanishing.

Cited by 2 publications

References 24 publications

The relative trace formula in analytic number theory

The relative trace formula in analytic number theory

On the Gross-Prasad conjecture with its refinement for $\left(\mathrm{SO}\left(5\right),\mathrm{SO}\left(2\right)\right)$ and the generalized Böcherer conjecture

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