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Some applications of modular units

Published online by Cambridge University Press:  03 June 2015

Ick Sun Eum
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon 305–701, Republic of Korea (zandc@kaist.ac.kr; jkkoo@math.kaist.ac.kr)
Ja Kyung Koo
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon 305–701, Republic of Korea (zandc@kaist.ac.kr; jkkoo@math.kaist.ac.kr)
Dong Hwa Shin
Affiliation:
Department of Mathematics, Hankuk University of Foreign Studies, Yongin-si, Gyeonggi-do 449–791, Republic of Korea (dhshin@hufs.ac.kr)
Corresponding

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 .

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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References

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