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math.NT2024

Co-rank Arithmetic Siegel--Weil IV: Analytic local-to-global

Ryan C. Chen

This is the fourth in a sequence of four papers, where we prove the arithmetic Siegel--Weil formula in co-rank for Kudla--Rapoport special cycles on exotic smooth integral mode…

math.NT2024

Co-rank Arithmetic Siegel--Weil III: Geometric local-to-global

Ryan C. Chen

This is the third in a sequence of four papers, where we prove the arithmetic Siegel--Weil formula in co-rank for Kudla--Rapoport special cycles on exotic smooth integral model…

math.NT2024

Co-rank Arithmetic Siegel--Weil II: Local Archimedean

Ryan C. Chen

This is the second in a sequence of four papers, where we prove the arithmetic Siegel--Weil formula in co-rank for Kudla--Rapoport special cycles on exotic smooth integral mode…

math.NT2024

Co-rank Arithmetic Siegel--Weil I: Local non-Archimedean

Ryan C. Chen

This is the first in a sequence of four papers, where we prove the arithmetic Siegel--Weil formula in co-rank for Kudla--Rapoport special cycles on exotic smooth integral model…

math.NT2019

A Refined Conjecture for the Variance of Gaussian Primes Across Sectors

Ryan C. Chen, Yujin H. Kim, Jared D. Lichtman +6

We derive a refined conjecture for the variance of Gaussian primes across sectors, with a power saving error term, by applying the L-functions Ratios Conjecture. We observe a bifur…

math.NT2018

-adic Properties of Hauptmoduln with Applications to Moonshine

Ryan C. Chen, Samuel Marks, Matthew Tyler

The theory of monstrous moonshine asserts that the coefficients of Hauptmoduln, including the -function, coincide precisely with the graded characters of the monster module, an…