T. Daniels

collaborators

5 papers

math.NT2026

Vanishing Coefficients in Products of Quintuple Products

Taylor Daniels, Tim Huber, James McLaughlin +1

Explicit arithmetic progressions modulo primes $p \equiv 1 (mod 4)$ are derived in which the coefficients in the expansions of products of quintuple products vanish. In particular…

math.NT2026

The $p$ -Dissection of a Product of Quintuple Products

Taylor Daniels, Timothy Huber, James McLaughlin +1

Let $p \equiv 1 (mod 4)$ be prime, let $m$ and $n$ be integers such that $p = m^{2} + n^{2}$ , and let $b$ be a positive integer. Let $Q(z,q) = (z,q/z,q;q)_{\infty}(qz^2,q/z^2;q^2)_{\infty…

math.NT2026

Periodic vanishings of the Legendre-17 signed partition numbers

Taylor Daniels

For $f : N \to {0, \pm 1}$ the $f$ -signed partition numbers $p (n, f)$ are defined to be the weighted partition sums \[ \mathfrak{p}(n,f) = \sum_{\substack{x_{1}…

math.NT2024

Legendre-signed partition numbers

Taylor Daniels

Let $f : N \to {0, \pm 1}$ , for $n \in N$ let $I^[n]$ be the set of partitions of $n$ , and for all partitions $I ¨ = (a_{1}, a_{2}, \dots, a_{k}) \in I^[n]$ let \[ f(Ï) := f(…

math.NT2024

Vanishing coefficients in two $q$ -series related to Legendre-signed partitions

Taylor Daniels

We demonstrate some 10-periodic properties of the coefficients of two $q$ -series related to partition numbers signed by the Legendre symbol $(\frac{a}{5})$ and to the Rogers-Ramanu…

Vanishing Coefficients in Products of Quintuple Products

The p-Dissection of a Product of Quintuple Products

Periodic vanishings of the Legendre-17 signed partition numbers

Legendre-signed partition numbers

Vanishing coefficients in two q-series related to Legendre-signed partitions

The $p$ -Dissection of a Product of Quintuple Products

Vanishing coefficients in two $q$ -series related to Legendre-signed partitions