arXiv subjects

Murilo Corato-Zanarella

Publications and source records attributed to Murilo Corato-Zanarella.

3 recordsLinked to original sources

arXiv2026

First explicit reciprocity law for unitary Friedberg--Jacquet periods

Consider a unitary group $G(\mathbb{A}_{F^+})=U_{2r}(\mathbb{A}_{F^+})$ over a CM extension $F/F^+$ with $G(\mathbb{A}_\infty)$ compact. In this article, we study the Beilinson--Bloch--Kato conjecture for motives associated to irreducible cuspidal automorphic representations $\pi$ of $G(\mathbb{A}_{F^+}).$ We prove that if $\pi$ is distinguished by the unitary Friedberg--Jacquet period, then the Bloch--Kato Selmer group (with coefficients in a favorable field) of the motive of $\Pi=\mathrm{BC}(\pi)$ vanishes.

math.NT↗

arXiv2023

Spherical functions of symmetric forms and a conjecture of Hironaka

For all $r\ge1,$ we verify the following conjecture of Hironaka: for a $p$-adic field $F$ with $p$ odd, the space of spherical functions of $\mathrm{Sym}_{r\times r}(F)\cap\mathrm{GL}_r(F)$ is free of rank $4^r$ over the Hecke algebra.

math.NT↗

arXiv2023

Spherical functions on symmetric spaces of Friedberg-Jacquet type

We give explicit models for spherical functions on $p$-adic symmetric spaces $X=H\backslash G$ for pairs of $p$-adic groups $(G,H)$ of the form $(\mathrm{U}(2r),\mathrm{U}(r)\times \mathrm{U}(r)),$ $(\mathrm{O}(2r),\mathrm{O}(r)\times \mathrm{O}(r)),$ $(\mathrm{Sp}(4r),\mathrm{Sp}(2r)\times\mathrm{Sp}(2r))),$ $(\mathrm{U}(2r+1),\mathrm{U}(r+1)\times \mathrm{U}(r)),$ and $ (\mathrm{O}(2r+1),\mathrm{O}(r+1)\times \mathrm{O}(r)).$ As an application, we completely describe their Hecke module structure.

math.NT↗