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Shunsuke Yamana

Publications and source records attributed to Shunsuke Yamana.

10 recordsLinked to original sources
arXiv2025

$p$-adic $L$-functions for $\mathrm U(2,1)\times\mathrm U(1,1)$

We construct the five-variable $p$-adic $L$-function attached to Hida families on $\mathrm U(2,1)\times\mathrm U(1,1)$, interpolating the square-root of Rankin-Selberg $L$-values in the \emph{shifted piano} range. Our construction relies on a new theta operator and its $p$-adic variation which plays a role analogous to the classical Ramanujan-Serre theta operator in Hida's $p$-adic Rankin-Selberg method. The interpolation formula, including the modified Euler factors at $p$ and at the real place, is consistent with the conjectural shape of $p$-adic $L$-functions predicted by Coates and Perrin-Riou.

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arXiv2023

Five-variable $p$-adic $L$-functions for $U(3)\times U(2)$

We construct a five-variable $p$-adic $L$-function attached to Hida families on the definite unitary groups $U(3)$ and $U(2)$ by using the Ichino-Ikeda formula. The interpolation formula fits into the conjectural shape of $p$-adic $L$-functions predicted by Coates and Perrin-Riou.

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arXiv2023

Four-variable $p$-adic triple product $L$-functions and the trivial zero conjecture

We construct the four-variable primitive $p$-adic $L$-functions associated with the triple product of Hida families and prove the explicit interpolation formulae at all critical values in the balanced range. Our construction is to carry out the $p$-adic interpolation of Garrett's integral representation of triple product $L$-functions via the $p$-adic Rankin-Selberg convolution method. As an application, we obtain the cyclotomic $p$-adic $L$-function for the motive associated with the triple product of elliptic curves and prove the trivial zero conjecture for this motive.

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arXiv2022

Bessel periods and anticyclotomic $p$-adic spinor $L$-functions

We construct the anticyclotomic $p$-adic $L$-function that interpolates a square root of central values of twisted spinor $L$-functions of a quadratic base change of a Siegel cusp form of genus $2$ with respect to a paramodular group of square-free level, assuming the Böcherer conjecture for the central $L$-values with anticyclotomic twists.

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arXiv2021

Restriction of Eisenstein series and Stark-Heegner points

In a recent work of Darmon, Pozzi and Vonk, the authors consider a particular $p$-adic family of Hilbert Eisenstein series $E_k(1,\brch)$ associated with an odd character $\brch$ of the narrow ideal class group of a real quadratic field $F$ and compute the first derivative of a certain one-variable twisted triple product $p$-adic $L$-series attached to $E_k(1,\brch)$ and an elliptic newform $f$ of weight $2$ on $Γ_0(p)$. In this paper, we generalize their construction to include the cyclotomic variable and thus obtain a two-variable twisted triple product $p$-adic $L$-series. Moreover, when $f$ is associated with an elliptic curve $E$ over $\Q$, we prove that the first derivative of this $p$-adic $L$-series along the weight direction is a product of the $p$-adic logarithm of a Stark-Heegner point of $E$ over $F$ introduced by Darmon and the cyclotomic $p$-adic $L$-function for $E$.

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arXiv2018

Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences

We give a formula for certain values and derivatives of Siegel series and use them to compute Fourier coefficients of derivatives of the Siegel Eisenstein series of weight g/2 and genus g. When g=4, the Fourier coefficient is approximated by a certain Fourier coefficient of the central derivative of the Siegel Eisenstein series of weight 2 and genus 3, which is related to the intersection of 3 arithmetic modular correspondences. Applications include a relation between weighted averages of representation numbers of symmetric matrices.

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arXiv2016

The CAP representations indexed by Hilbert cusp forms

We combine the Duke-Imamoglu-Ikeda lifting with the theta lifting to produce new CAP representations of metaplectic, symplectic and orthogonal groups. These constructions partially generalize the theories of Waldspurger on the Shimura correspondence and of Piatetski-Shapiro on the Saito-Kurokawa lifting to higher dimensions. Applications include a relation between Fourier coefficients of Hilbert cusp forms of weight k+1/2 and a weighted sum of the representation numbers of a quadratic form of rank 2k by a quadratic form of rank 4k.

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arXiv2008

Jacobi forms of degree one

We show that a certain subspace of space of elliptic cusp forms is isomorphic as a Hecke module to a certain subspace of space of Jacobi cusp forms of degree one with matrix index by constructing an explicit lifting. This is a partial generalization of the work of Skoruppa and Zagier. This lifting is also related with the Ikeda lifting.

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arXiv2008

Maass relations in higher genus

For an arbitrary even genus $2n$ we show that the subspace of Siegel cusp forms of degree $2n$ generated by Ikeda lifts of elliptic cusp forms can be characterized by certain linear relations among Fourier coefficients. This generatizes the work of Kohnen and Kojima.

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