Automorphic products that are singular modulo primes
Haowu Wang, Brandon Williams
TL;DR
This paper demonstrates that Fourier coefficients of reflective Borcherds products exhibit congruences modulo primes, using Rankin--Cohen brackets on orthogonal groups to establish these properties.
Contribution
It introduces a novel application of Rankin--Cohen brackets to analyze congruences of Fourier coefficients in automorphic products.
Findings
Fourier coefficients satisfy congruences modulo primes
Rankin--Cohen brackets are effective in this context
Reflective Borcherds products exhibit predictable modular behavior
Abstract
We use Rankin--Cohen brackets on O(n, 2) to prove that the Fourier coefficients of reflective Borcherds products often satisfy congruences modulo certain primes.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Finite Group Theory Research · Algebraic Geometry and Number Theory