arXiv subjects

Armando Gutierrez Terradillos

Publications and source records attributed to Armando Gutierrez Terradillos.

5 recordsLinked to original sources

arXiv2026

Relative Langlands duality of the Bump-Friedberg-Ginzburg $\mathrm{GSO}_6$-integral

We provide a new instance of singular relative Langlands duality, underlying a Rankin-Selberg integral on $\mathrm{GSO}_6$ due to Bump-Friedberg-Ginzburg. We conclude that this integral represents an essentially self-dual object in the relative Langlands program, and we demonstrate that the Langlands dual automorphic integral computes a finite sum of $L$-functions, reflecting stacky structure on the spectral side.

math.NT↗

arXiv2026

On Periods and $L$-functions for $\mathbf{GL}_4 \times \mathbf{GL}_2$

We give a new integral representation of the $\wedge^2 \otimes \mathrm{std}_2$ $L$-function of generic cusp forms on $\mathbf{GL}_4 \times \mathbf{GL}_2$ and $\mathbf{GU}_{2,2}\times \mathbf{GL}_2$. In the former case, we use it to prove a relation between its central $L$-value and the generalized Shalika period. Exploiting the theta correspondence for $(\mathbf{GL}_4,\mathbf{GL}_4)$, we further establish a relation between the central value of the $L$-function attached to the strongly tempered spherical pair $(\mathbf{GL}_4 \times \mathbf{GL}_2,\mathbf{GL}_2 \times \mathbf{GL}_2)$ and its corresponding period. In the case of cusp forms on $\mathbf{GL}_4 \times \mathbf{GL}_2$ that are unramified everywhere, our formulas give new evidence towards conjectures of Wan-Zhang and of Gan-Gross-Prasad for $\mathbf{GSpin}_6 \times \mathbf{GSpin}_3$.

math.NT↗

arXiv2025

Spherical Shalika models on $\mathrm{PGU}_{2,2}$ and the theta correspondence for $(\mathrm{PGSp}_4,\mathrm{PGU}_{2,2})$

We study Shalika models for generic unramified representations of $\mathrm{PGU}_{2,2}$ over non-archimedean local fields of characteristic zero. We show that they are unique up to constant by means of the theta correspondence for $(\mathrm{PGSp}_4,\mathrm{PGU}_{2,2})$. We then prove a Casselman-Shalika formula which relates the values of spherical Shalika functionals on ${\rm PGU}_{2,2}$ to the values of finite dimensional complex representations of the dual group of $\mathrm{PGSp}_4$.

math.NT↗

arXiv2025

A truncated Siegel-Weil formula and Borcherds forms

In this paper we use the regularized Siegel-Weil formula of Gan-Qiu-Takeda to obtain an expression of the integral of the theta function over the truncated modular curve. We apply this result to express the integral over the truncated modular curve of the logarithm of the Borcherds form and we describe explicitly its asymptotic behaviour, and in particular the convergent and divergent contributions. The result provides a complement to the work of Kudla on integrals of Borcherds forms in a limiting case which falls out the range of applications.

math.NT↗

arXiv2024

A two variable Rankin-Selberg integral for $\mathrm{GU}(2,2)$ and the degree 5 $L$-function of $\mathrm{GSp}_4$

We give a two-variable Rankin--Selberg integral for generic cusp forms on $\mathrm{PGL}_4$ and $\mathrm{PGU}_{2,2}$ which represents a product of exterior square $L$-functions. As a residue of our integral, we obtain an integral representation on $\mathrm{PGU}_{2,2}$ of the degree 5 $L$-function of $\mathrm{GSp}_4$ twisted by the quadratic character of $E/F$ of cuspidal automorphic representations which contribute to the theta correspondence for the pair $(\mathrm{PGSp}_4,\mathrm{PGU}_{2,2})$.

math.NT↗