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Some applications of modular units

Part of: Discontinuous groups and automorphic forms Arithmetic algebraic geometry

Published online by Cambridge University Press:  03 June 2015

Ick Sun Eum ,
Ja Kyung Koo  and
Dong Hwa Shin
Ick Sun Eum
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon 305–701, Republic of Korea ([email protected]; [email protected])
Ja Kyung Koo
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon 305–701, Republic of Korea ([email protected]; [email protected])
Dong Hwa Shin
Affiliation:
Department of Mathematics, Hankuk University of Foreign Studies, Yongin-si, Gyeonggi-do 449–791, Republic of Korea ([email protected])
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Abstract

We show that a weakly holomorphic modular function can be written as a sum of modular units of higher level. Furthermore, we find a necessary and sufficient condition for a meromorphic Siegel modular function of degree g to have neither a zero nor a pole on a certain subset of the Siegel upper half-space .

Keywords

modular unitsmodular functionsSiegel modular forms

MSC classification

Secondary: 11G16: Elliptic and modular units 11F03: Modular and automorphic functions 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 1 , February 2016 , pp. 91 - 106
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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