PreprintCC0arXiv
Modular L-functions and Chebyshev systems
Abstract
We study real zeros of completed modular L-functions and the determination of cusp forms by their periods. Using Chebyshev systems and the Riemann-Roch theorem, we obtain bounds for real zeros, counted with multiplicity, and rank estimates for evaluation maps in terms of the dimensions of cusp-form spaces and the genera of modular curves. These estimates give criteria for finite families of periods to determine a cusp form and yield explicit dual bases in cases where the relevant quotient curves have genus zero. We also bound the dimensions of rational spans of eigenform periods.
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BibTeX
@misc{wang2026modular,
title = {{Modular L-functions and Chebyshev systems}},
author = {Wei Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02933},
eprint = {2611.02933},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02933},
note = {CC0},
}
RIS
TY - UNPB
TI - Modular L-functions and Chebyshev systems
AU - Wei Wang
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02933
UR - https://arxiv.org/abs/2611.02933
AB - We study real zeros of completed modular L-functions and the determination of cusp forms by their periods. Using Chebyshev systems and the Riemann-Roch theorem, we obtain bounds for real zeros, counted with multiplicity, and rank estimates for evaluation maps in terms of the dimensions of cusp-form spaces and the genera of modular curves. These estimates give criteria for finite families of periods to determine a cusp form and yield explicit dual bases in cases where the relevant quotient curves have genus zero. We also bound the dimensions of rational spans of eigenform periods.
ER -