Masaaki Furusawa

On central critical values of the degree four L-functions for GSp (4): the fundamental lemma, II

We propose a new relative trace formula concerning the central critical values of the spinor

On the global Gross-Prased conjecture for Yoshida liftings

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The fundamental lemma for the Bessel and Novodvorsky subgroups of GSp(4) II

-functions for GSp (4). The main result is a proof of the fundamental lemma for the unit element of the Hecke algebra. Our new relative trace formula has some significant advantages over the previous ones for the subsequent development.

On inversion of the bessel and gelfand transforms

We restrict a Siegel modular cusp form of degree 2 and square free level that is a Yoshida lifting (a lifting from the orthogonal group of a definite quaternion algebra) to the embedded product of two half planes and compute the Petersson product against the product of two elliptic cuspidal Hecke eigenforms. The square of this integral can be explicitly expressed in terms of the central critical value of an L-function attached to the situation. The result is related to a conjecture of Gross and Prasad about restrictions of automorphic representations of special orthogonal groups.

On special values of certain L-functions

Abstract We announce, in the case of the group GSp(4), an equality of two local integrals. One is a Kloosterman integral on the Bessel subgroups of GSp(4) and the other is a Kloosterman integral on the Novodvorsky subgroups of GSp(4). We conjecture that Jacquets relative trace formula for GL(2) in [7], where Jacquet has given another proof of Waldspurgers result [9], generalizes to GSp(4). We believe that this approach will lead us to a proof and also a precise formulation of a conjecture of Bocherer [1]. Support for this conjecture may be found in the important paper of Bocherer and Schulze-Pillot [2]. Our result serves as the fundamental lemma for our conjectural relative trace formula for the main relevant double cosets.

On central critical values of the degree four -functions for GSp(4): the fundamental lemma

We construct the Plancherel measure corresponding to the Bessel model on the split special orthogonal group of odd degree > 5 and the Whit-taker model on a connected split reductive group in general. As an application we prove the inversion formula which expresses the related integral transform in terms of the Satake transform.

On central critical values of the degree four \(L\)-functions for \({\text {GSp}}\left( 4\right) \): a simple trace formula

We prove an algebraicity result concerning special values of certain automorphic

On special Bessel periods and the Gross-Prasad conjecture for SO(2n + 1) × SO(2)

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Refined global Gross-Prasad conjecture on special Bessel periods and B\"ocherer's conjecture

-functions. Namely let

Local root numbers, Bessel models, and a conjecture of Guo and Jacquet

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