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Texas A&M University

Number Theory Seminar

Date: December 1, 2021

Time: 11:00AM - 12:00PM

Location: BLOC 302

Speaker: Riad Masri, Texas A&M University


Title: The distribution of short orbits of singular moduli

Abstract: The values of the modular j-function at CM points are algebraic numbers called singular moduli. There is a natural action of the class group G(d) of discriminant d on the set of singular moduli. For each d, fix a singular modulus j(d,0) and a subgroup H(d) < G(d). Let Av(d,0) denote the average of the numbers in the orbit H(d)*j(d,0). Under a mild growth condition on |H(d)|, we will compute the distribution of Av(d,0) as |d| approaches infinity. Our growth condition is expressed as a function of the best progress towards the Lindelöf hypothesis for modular L-functions. This is joint work with Annika Mauro and Tanis Nielsen.