Kilian Rausch

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20192026

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math.NT2026

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 $ω_{k + 1, D}$ studied by Mono, Rolen, and the second author, we introduce two further fun…

math.NT2026

The difference of the sums of odd and even parts of restricted partitions

Kilian Rausch, Johann Stumpenhusen

For a subset $D \subset N$ , denote by $S (D, n)$ the total sum of all odd parts minus the sum of all even parts of all partitions of $n$ in which parts from $D$ d…

math.NT2026

A Rademacher exact type formula for pod $_{2} (n)$

Kilian Rausch

In this paper, we calculate an exact formula for the number of partitions of a natural number $n$ , where the largest part is even and no odd parts appears more than two times. The…

math.NT2025

Mock modular forms from the k-rank moments

Kilian Rausch

In this paper, the generating functions of Garvans so-called $k$ -ranks are used, to define a family of mock Eisenstein series. The $k$ -rank moments are then expressed as partition…

Local Weak Maass Forms and Traces of Cycle Integrals

The difference of the sums of odd and even parts of restricted partitions

A Rademacher exact type formula for pod2​(n)

Mock modular forms from the k-rank moments

A Rademacher exact type formula for pod $_{2} (n)$