10 citations · 25 across the 7 of their papers we have counts for
10 papers
Indefinite Theta Series on Cones
Martin Westerholt-Raum
We show that indefinite theta series on cones converge and provide an explicit modular completion. Our completion rests on a convolution of the Gaussian with a piecewise constant f…
HLinear: Exact Dense Linear Algebra in Haskell
Alexandru Ghitza, Martin Raum
We present an implementation in the functional programming language Haskell of the PLE decomposition of matrices over division rings. Our benchmarks indicate that it is competitive…
Almost holomorphic Poincare series corresponding to products of harmonic Siegel-Maass forms
K. Bringmann, O. K. Richter, M. Westerholt-Raum
We investigate Poincaré series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the pro…
Harmonic Weak Siegel Maaß Forms I
Martin Westerholt-Raum
Given a non-holomorphic Saito-Kurokawa lift we construct a preimage under the vector-valued lowering operator. In analogy with the case of harmonic weak elliptic Maaß forms, this p…
Direct Integration for Mirror Curves of Genus Two and an Almost Meromorphic Siegel Modular Form
Albrecht Klemm, Maximilian Poretschkin, Thorsten Schimannek +1
This work considers aspects of almost holomorphic and meromorphic Siegel modular forms from the perspective of physics and mathematics. The first part is concerned with (refined) t…
Sturm Bounds for Siegel Modular Forms
Olav K. Richter, Martin Westerholt-Raum
We establish Sturm bounds for degree g Siegel modular forms modulo a prime p, which are vital for explicit computations. Our inductive proof exploits Fourier-Jacobi expansions of S…
Products of Vector Valued Eisenstein Series
Martin Westerholt-Raum
We prove that products of at most two vector valued Eisenstein series that originate in level 1 span all spaces of cusp forms for congruence subgroups. This can be viewed as an ana…
Kudla's Modularity Conjecture and Formal Fourier-Jacobi Series
Jan Hendrik Bruinier, Martin Westerholt-Raum
We prove modularity of formal series of Jacobi forms that satisfy a natural symmetry condition. They are formal analogues of Fourier-Jacobi expansions of Siegel modular forms. From…
Formal Fourier Jacobi Expansions and Special Cycles of Codimension 2
Martin Raum
We prove that formal Fourier Jacobi expansions of degree 2 are Siegel modular forms. As a corollary, we deduce modularity of the generating function of special cycles of codimensio…
H-Harmonic Maass-Jacobi Forms of Degree 1: The Analytic Theory of Some Indefinite Theta Series
Martin Westerholt-Raum
It was shown in previous work that the one-variable -function defined by Zwegers (and Zagier) and his indefinite theta series attached to lattices of signature $(r\!+\!1…