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Generation of Siegel modular function fields of even level


Author: Dong Sung Yoon
Journal: Proc. Amer. Math. Soc. 146 (2018), 921-931
MSC (2010): Primary 11F46; Secondary 14K25
DOI: https://doi.org/10.1090/proc/13768
Published electronically: September 13, 2017
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Abstract: For positive integers $ g$ and $ N$, let $ \mathcal {F}_N^{(g)}$ be the field of meromorphic Siegel modular functions of genus $ g$ and level $ N$ whose Fourier coefficients belong to the $ N$th cyclotomic field. We construct explicit generators of $ \mathcal {F}_N^{(g)}$ over $ \mathcal {F}_1^{(g)}$ by making use of a quotient of theta constants, when $ g\geq 2$ and $ N$ is even.


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Additional Information

Dong Sung Yoon
Affiliation: Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea
Email: math_dsyoon@kaist.ac.kr

DOI: https://doi.org/10.1090/proc/13768
Keywords: Siegel modular functions, theta constants
Received by editor(s): September 7, 2016
Received by editor(s) in revised form: April 5, 2017
Published electronically: September 13, 2017
Additional Notes: The author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03030015).
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2017 American Mathematical Society

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