Robert Dicks

activity

20152026

most citedCongruences between word length statistics for the finitary alternating and symmetric groups

2 citations · 2 across the 9 of their papers we have counts for

collaborators

12 papers

math.NT2026

Quadratic Congruences for half-integral weight cusp forms with the eta multiplier

Robert Dicks

Let $ℓ \geq 5$ be a prime, and let $ν_{η}$ denote the Dedekind eta multiplier. For an odd integer $r$ , and a real Dirichlet character $ψ$ , recent work of Ahlgren, Andersen, and th…

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…

math.NT2025

Zeros of symmetric power period polynomials

Robert Dicks, Hui Xue

Suppose that $k$ and $N$ are positive integers. Let $f$ be a newform on $Γ_{0} (N)$ of weight $k$ with $L$ -function $L_{f} (s)$ . Previous works have studied the zeros of the period polyn…

math.NT2023

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…

math.NT2022

Congruence relations for r-colored partitions

Robert Dicks

Let $ℓ \geq 5$ be prime. For the partition function $p (n)$ and $5 \leq ℓ \leq 31$ , Atkin found a number of examples of primes $Q \geq 5$ such that there exist congruences of…

math.NT2022

Integer partitions with large Dyson rank

Colin Alberts, Olivia Beckwith, Irfan Demetoglu +3

The Dyson rank of an integer partition is the difference between its largest part and the number of parts it contains. Using Fine-Dyson symmetry, we give formulas for the number of…