PreprintCC BY 4.0arXiv
Modular Forms Related to Real Quadratic Fields as Traces of Cycle Integrals
Abstract
A decade ago, locally harmonic Maaß forms were first established by Bringmann, Kane, and Kohnen in negative weights and independently by Hövel in weight $0$. Since then, they have seen important applications related to twisted central L-values of newforms. However, there are just a few examples of these forms known so far, and in particular there is no unifying theory behind these examples. Towards this direction, we show that the representations of Zagier's fk,D and Mono's gk+1,D functions as traces of cycle integrals are not unique.
Related
- Zeta elements for p-ordinary modular forms over imaginary quadratic fields and applications
- Local Weak Maass Forms and Traces of Cycle Integrals
- Quasi-modularity of q-traces and integrals over Hilbert schemes
- From quadratic integrals to Nijenhuis operators: two-dimensional dictionary
- Modular integrals for individual modular knots
BibTeX
@misc{stumpenhusen2026modular,
title = {{Modular Forms Related to Real Quadratic Fields as Traces of Cycle Integrals}},
author = {Johann Stumpenhusen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.24373},
eprint = {2608.24373},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24373},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Modular Forms Related to Real Quadratic Fields as Traces of Cycle Integrals
AU - Johann Stumpenhusen
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2608.24373
UR - https://arxiv.org/abs/2608.24373
AB - A decade ago, locally harmonic Maaß forms were first established by Bringmann, Kane, and Kohnen in negative weights and independently by Hövel in weight $0$. Since then, they have seen important applications related to twisted central L-values of newforms. However, there are just a few examples of these forms known so far, and in particular there is no unifying theory behind these examples. Towards this direction, we show that the representations of Zagier's f_k,D and Mono's g_k+1,D functions as traces of cycle integrals are not unique.
ER -