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Vector Valued Katok-Sarnak Formulas
Abstract
We introduce a version of the Katok-Sarnak formula linking twisted traces of scalar valued Maass cusp forms for Γ0(N) with N square-free to Fourier coefficients of vector valued Maass cusp forms for the metaplectic group Mp2(ℤ) and the Weil representation associated to a lattice of signature (2,1). We prove this by computing the Fourier coefficients of the vector valued Siegel and Millson theta lift of a scalar valued newform by two different methods and comparing the results.
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BibTeX
@misc{strathausen2026vector,
title = {{Vector Valued Katok-Sarnak Formulas}},
author = {Rebekka Strathausen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41298},
eprint = {2610.41298},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41298},
}
RIS
TY - UNPB
TI - Vector Valued Katok-Sarnak Formulas
AU - Rebekka Strathausen
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41298
UR - https://arxiv.org/abs/2610.41298
AB - We introduce a version of the Katok-Sarnak formula linking twisted traces of scalar valued Maass cusp forms for Γ_0(N) with N square-free to Fourier coefficients of vector valued Maass cusp forms for the metaplectic group Mp_2(ℤ) and the Weil representation associated to a lattice of signature (2,1). We prove this by computing the Fourier coefficients of the vector valued Siegel and Millson theta lift of a scalar valued newform by two different methods and comparing the results.
ER -