Michael A. Daas

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20232026

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math.NT2026

Beyond the Giampietro--Darmon Conjecture

Michael A. Daas

Giampietro and Darmon conjectured a formula for the norm of various algebraic numbers, obtained as infinite products of $p$ -adic cross-ratios of CM points. These quantities arose f…

math.NT2025

Congruence conditions for the mod $λ$ values of the Fourier coefficients of classical eigenforms

Michael A. Daas

We classify all instances of the condition $a_{p} (f) \equiv x mod λ$ being related to a congruence on the prime $p$ , where $a_{p} (f)$ denotes the $p$ th Fourier coefficient of a c…

math.NT2023

CM-values of $p$ -adic $Θ$ -functions

Michael A. Daas

We prove a $p$ -adic version of the work by Gross and Zagier on the differences between singular moduli by proving a set of conjectures by Giampietro and Darmon, who investigated th…

Beyond the Giampietro--Darmon Conjecture

Congruence conditions for the mod λ values of the Fourier coefficients of classical eigenforms

CM-values of p-adic Θ-functions

Congruence conditions for the mod $λ$ values of the Fourier coefficients of classical eigenforms

CM-values of $p$ -adic $Θ$ -functions