3 papers
math.NT2025
Arithmetic properties of generalized Frobenius partitions
Scott Ahlgren, Cruz Castillo
Ramanujan proved three famous congruences for the partition function modulo 5, 7, and 11. The first author and Boylan proved that these congruences are the only ones of this type.…
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.NT2014
Dissections of a "strange" function
Scott Ahlgren, Byungchan Kim
The "strange" function of Kontsevich and Zagier is defined by \[F(q):=\sum_{n=0}^\infty(1-q)(1-q^2)\dots(1-q^n).\] This series is defined only when is a root of unity, and prov…