From the 1 of 6 linked papers with an AI index.
6 papers
Submultiplicative Polynomials in Combinatorics
Krystian Gajdzica, Bernhard Heim, Markus Neuhauser +1
The paper defines recursively constructed polynomials from normalized sequences and investigates when they satisfy a submultiplicative inequality similar to the Bessenrodt–Ono ineq…
Dominant Zeros of Nekrasov--Okounkov Polynomials
Bernhard Heim, Markus Neuhauser, with an appendix by Ken Ono
We give an exact finite-dimensional Perron--Frobenius realization of the dominant zero of the Nekrasov--Okounkov polynomials $\nop _n(z)$. For a normalized positive sequence $h=(h(…
Polynomization of Sun's Conjecture
Bernhard Heim und Markus Neuhauser
Let denote the number of partitions of a natural number . As , the th root of tends to , which is related to the Cauchy--Hadamard test for pow…
On the Detection of Non-Roots of D'Arcais Polynomials
Bernhard Heim, Johann Stumpenhusen
The Lehmer conjecture states that the non-constant Fourier coefficients of the 24th power of the Dedekind eta function are non-zero. In a recent preprint, Neuhauser and the first a…
Log-Concavity and Log-Convexity of Restricted Infinite Products
Krystian Gajdzica, Bernhard Heim, Markus Neuhauser
In this paper we provide a classification on the sign distribution of , where \begin{equation*} \sum_{n =0…
On the Non-vanishing of the D'Arcais Polynomials
Bernhard Heim, Markus Neuhauser
In this paper we invest in the non-vanishing of the Fourier coefficients of powers of the Dedekind eta function. This is reflected in non-vanishing properties of the D'Arcais polyn…