From the 1 of 6 linked papers with an AI index.
6 papers
Modular Forms Related to Real Quadratic Fields as Traces of Cycle Integrals
Johann Stumpenhusen
A decade ago, locally harmonic Maaß forms were first established by Bringmann, Kane, and Kohnen in negative weights and independently by Hövel in weight . Since then, they have…
On the Log-Concavity of the D'Arcais Polynomials for Normalised Functions
Johann Stumpenhusen
The paper introduces a new variant of log‑concavity for families of polynomials and proves that specific D'Arcais polynomials satisfy this property at particular points.
The difference of the sums of odd and even parts of restricted partitions
Kilian Rausch, Johann Stumpenhusen
For a subset , denote by the total sum of all odd parts minus the sum of all even parts of all partitions of in which parts from d…
On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials
Steven Charlton, Bernhard Heim, Johann Stumpenhusen
Recently, Starr used asymptotic methods to disprove a conjecture by Heim--Neuhauser and Abdesselam about the log-concavity of the D'Arcais polynomials, without giving an explicit c…
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…
On a Divisor Modular Form and a Theta Lift
Andreas Mono, Larry Rolen, Johann Stumpenhusen
In 1975, Zagier introduced the highly influential hyperbolic Poincaré series . We connect the divisor modular form of to a new weak Maass form . Fur…