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

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12 papers · 1 filter

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…

math.NT2021

Weight 2 CM newforms as p-adic limits

Robert Dicks

Previous works have shown that certain weight $2$ newforms are $p$ -adic limits of weakly holomorphic modular forms under repeated application of the $U$ -operator. The proofs of the…

math.NT2020

Congruences for Level $1$ cusp forms of half-integral weight

Robert Dicks

Suppose that $ℓ \geq 5$ is prime. For a positive integer $N$ with $4 ∣ N$ , previous works studied properties of half-integral weight modular forms on $Γ_{0} (N)$ which are suppo…

math.NT2020

A Higher Weight Analogue of Ogg's Theorem on Weierstrass Points

Robert Dicks

For a positive integer $N$ , we say that $\infty$ is a Weierstrass point on the modular curve $X_{0} (N)$ if there is a non-zero cusp form of weight $2$ on $Γ_{0} (N)$ which vanishes at $…

math.NT2016

Asymptotics and congruences for partition functions which arise from finitary permutation groups

Tessa Cotron, Robert Dicks, Sarah Fleming

In a recent paper, Bacher and de la Harpe study the conjugacy growth series of finitary permutation groups. In the course of studying the coefficients of a series related to the fi…

math.NT2016★ 2 cited

Congruences between word length statistics for the finitary alternating and symmetric groups

Tessa Cotron, Robert Dicks, Sarah Fleming

In a recent paper, Bacher and de la Harpe study conjugacy growth series of infinite permutation groups and their relationships with $p (n)$ , the partition function, and $p(n)_{\text…

math.NT2015

Shifted distinct-part partition identities in arithmetic progressions

Ethan Alwaise, Robert Dicks, Jason Friedman +6

The partition function $p (n)$ , which counts the number of partitions of a positive integer $n$ , is widely studied. Here, we study partition functions $p_{S} (n)$ that count partitions…

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

Congruences like Atkin's for generalized Frobenius partitions

Zeros of symmetric power period polynomials

The Shimura lift and congruences for modular forms with the eta multiplier

Congruence relations for r-colored partitions

Integer partitions with large Dyson rank

Weight 2 CM newforms as p-adic limits

Congruences for Level 1 cusp forms of half-integral weight

A Higher Weight Analogue of Ogg's Theorem on Weierstrass Points

Asymptotics and congruences for partition functions which arise from finitary permutation groups

Congruences between word length statistics for the finitary alternating and symmetric groups

Shifted distinct-part partition identities in arithmetic progressions

Congruences for Level $1$ cusp forms of half-integral weight