6 papers
L-series of Eisenstein series vanishing at critical values
Johann Franke
Using the relations between rational functions and Eisenstein series, as well as the inferences for cotangent sums and period polynomials, we work out a precise description for Eis…
On the number of irreducible representations of
Walter Bridges, Kathrin Bringmann, Johann Franke
In this note, we use a variant of the hyperbola method to prove an asymptotic expansion for the summatory function of the number of irreducible -representations o…
Asymptotic expansions for partitions generated by infinite products
Walter Bridges, Benjamin Brindle, Kathrin Bringmann +1
Recently, Debruyne and Tenenbaum proved asymptotic formulas for the number of partitions with parts in () and good analytic prop…
Sign changes in statistics for plane partitions
Walter Bridges, Johann Franke, Joshua Males
Recent work of Cesana, Craig and the third author shows that the trace of plane partitions is asymptotically equidistributed in residue classes mod . Applying a technique of the…
Asymptotics for the twisted eta-product and applications to sign changes in partitions
Walter Bridges, Johann Franke, Taylor Garnowski
We prove asymptotic formulas for the complex coefficients of , where is a root of unity, and apply our results to determine secondary terms in the asymptoti…
An asymptotic formula for the number of -dimensional representations of
Kathrin Bringmann, Johann Franke
We prove an asymptotic formula for the number of -dimensional representations of the group . Main tools for the proof are Wright's Circle Method and the Saddle P…