6 papers
Vanishing Coefficients in Products of Quintuple Products
Taylor Daniels, Tim Huber, James McLaughlin +1
Explicit arithmetic progressions modulo primes are derived in which the coefficients in the expansions of products of quintuple products vanish. In particular…
The -Dissection of a Product of Quintuple Products
Taylor Daniels, Timothy Huber, James McLaughlin +1
Let be prime, let and be integers such that , and let be a positive integer. Let $Q(z,q) = (z,q/z,q;q)_{\infty}(qz^2,q/z^2;q^2)_{\infty…
Periodic vanishings of the Legendre-17 signed partition numbers
Taylor Daniels
For the -signed partition numbers are defined to be the weighted partition sums \[ \mathfrak{p}(n,f) = \sum_{\substack{x_{1}…
Legendre-signed partition numbers
Taylor Daniels
Let , for let be the set of partitions of , and for all partitions let \[ f(Ï) := f(…
Vanishing coefficients in two -series related to Legendre-signed partitions
Taylor Daniels
We demonstrate some 10-periodic properties of the coefficients of two -series related to partition numbers signed by the Legendre symbol and to the Rogers-Ramanu…
Bounds on the Möbius-signed partition numbers
Taylor Daniels
For let denote the set of partitions of , i.e., the set of positive integer tuples such that $x_1 \geq x_2 \geq \cdots \geq x_k…