Anton Hilado

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math.NT2025

Fourier Coefficients and Algebraic Cusp Forms on $U (2, n)$

Anton Hilado, Finn McGlade, Pan Yan

We establish a theory of scalar Fourier coefficients for a class of non-holomorphic, automorphic forms on the quaternionic real Lie group $U (2, n)$ . By studying the theta l…

math.NT2025

The Statement of Mochizuki's Corollary 3.12: Initial Theta Data

Taylor Dupuy, Anton Hilado

We show that Mochizuki's initial theta data is computable from an elliptic curve defined over $Q$ . We work out the case of initial theta data for the elliptic curve with C…

math.NT2024

Ford Spheres in the Clifford-Bianchi Setting

Spencer Backman, Taylor Dupuy, Anton Hilado +1

We define Ford Spheres $P$ in hyperbolic $n$ -space associated to Clifford-Bianchi groups $P S L_{2} (O)$ for $O$ orders in rational Clifford algebras associated to positive de…

math.NT2024

The Basic Theory of Clifford-Bianchi Groups for Hyperbolic n-Space

Taylor Dupuy, Anton Hilado, Colin Ingalls +1

Let $K$ be a $Q$ -Clifford algebra associated to an $(n - 1)$ -ary positive definite quadratic form and let $O$ be a maximal order in $K$ . A Clifford-Bianchi group i…

Fourier Coefficients and Algebraic Cusp Forms on U(2,n)

The Statement of Mochizuki's Corollary 3.12: Initial Theta Data

Ford Spheres in the Clifford-Bianchi Setting

The Basic Theory of Clifford-Bianchi Groups for Hyperbolic n-Space

Fourier Coefficients and Algebraic Cusp Forms on $U (2, n)$