Scott Ahlgren

collaborators

4 papers

math.NT2025

Eisenstein series modulo prime powers

Scott Ahlgren, Cruz Castillo, Clayton Williams

If $p \geq 5$ is prime and $k \geq 4$ is an even integer with $(p - 1) ∤ k$ we consider the Eisenstein series $G_{k}$ on $SL_{2} (Z)$ modulo powers of $p$ . It is…

math.NT2025

Scarcity of partition congruences on semiprime progressions

Scott Ahlgren, Olivia Beckwith

In recent work with Raum the authors considered congruences for the ordinary partition function $p (n)$ of the form $p (ℓ Q^{r} n + I^^{2}) \equiv 0 (mod ℓ)$ where $ℓ, Q \geq 5$ are pri…

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 $ℓ \leq 31$ for the partition function $p (n)$ in arithmetic progressions modulo $ℓ Q^{3}$ , where $Q \neq = ℓ$ is prime. R…