3 papers
math.NT2025
Congruences like Atkin's for generalized Frobenius partitions
Scott Ahlgren, Nickolas Andersen, Robert Dicks
In the 1960s Atkin discovered congruences modulo primes for the partition function in arithmetic progressions modulo , where is prime. R…
math.NT2024
Modular invariants for real quadratic fields and Kloosterman sums
Nickolas Andersen, William Duke
We investigate the asymptotic distribution of integrals of the -function that are associated to ideal classes in a real quadratic field. To estimate the error term in our asympt…
math.NT2024
The Shimura lift and congruences for modular forms with the eta multiplier
Scott Ahlgren, Nickolas Andersen, Robert Dicks
The Shimura correspondence is a fundamental tool in the study of half-integral weight modular forms. In this paper, we prove a Shimura-type correspondence for spaces of half-integr…