12 papers
Local Weak Maass Forms and Traces of Cycle Integrals
Kilian Rausch, Johann Stumpenhusen
Using relations established by Bringmann and Kane in a recent preprint based on the function studied by Mono, Rolen, and the second author, we introduce two further fun…
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…
A Positive Proportion of the Reduced D'Arcais Polynomials is not Hurwitz
Steven Charlton, Bernhard Heim, Markus Neuhauser +2
Heretofore, the second and third author conjectured that the D'Arcais polynomials, related to the coefficients of the powers of the Dedekind -function, are Hurwitz polynomials e…
On the Log-Concavity of the D'Arcais Polynomials for Normalised Functions
Johann Stumpenhusen
A sequence of non-negative real numbers is called log-concave at if . This property has been generalised in various ways t…
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 . Furth…
On the Gaussian Moat Problem
Johann Christian Stumpenhusen
The Gaussian Moat Problem asks whether it is possible to walk from the origin to infinity in the complex plane using only Gaussian primes as stepstones and steps of bounded length.…
On the Proportion of Coprime Fractions in Number Fields
Walter Bridges, Johann Franke, Johann Christian Stumpenhusen
In this paper we determine the asymptotic density of coprime fractions in those of the reduced fractions of number fields. When ordered by norms of denominators, we count a fractio…
On the solutions of
Johann Christian Stumpenhusen
This is a short note about a chapter in the author's bachelor thesis regarding a paper by Ford concerning a conjecture by Erdős.
Perfect Eisenstein integers
Johann Christian Stumpenhusen
We generalise the sum-of-divisors-function and evenness to the rings of integers of certain algebraic number fields. In particular, we present necessary and sufficient conditio…