Sean Howe

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math.NT2025

The completed Kirillov model and local-global compatibility for functions on Igusa varieties

Sean Howe

We describe the cuspidal functions $V_{b}^{cusp}$ on the ordinary Caraiani-Scholze Igusa variety for $GL_{2}$ as a completion of the smooth Kirillov model fo…

math.NT2025

Random matrix statistics and zeroes of $L$ -functions via probability in $I^»$ -rings

Sean Howe

We introduce a theory of probability in $I^»$ -rings designed to efficiently describe random variables valued in multisets of complex numbers, varieties over a field, or other simila…

math.NT2025

Equidistribution and arithmetic $I^$ -distributions

Matthew Bertucci, Sean Howe

We formulate an abstract notion of equidistribution for families of $I^»$ -probability spaces parameterized by admissible $Z$ -sets. Under the assumption of equidistribution,…

The completed Kirillov model and local-global compatibility for functions on Igusa varieties

Random matrix statistics and zeroes of L-functions via probability in I^»-rings

Equidistribution and arithmetic I^-distributions

Random matrix statistics and zeroes of $L$ -functions via probability in $I^»$ -rings

Equidistribution and arithmetic $I^$ -distributions