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 Arithmetic of the modular functions $j_{1,2}$ and $j_{1,3}$ Bull. Korean Math. Soc. 2007 Vol. 44, No. 1, 47-59 Printed March 1, 2007 Chang Heon Kim and Ja Kyung Koo Seoul Women's University, Korea Advanced Institute of Science and Technology Abstract : We find the uniformizers of modular curves $X_1(N)$ ($N=2,3$) and explore the relationship with Thompson series and number theoretic property. Keywords : modular curve, uniformizer, normalized generator, Thompson series MSC numbers : 11F03, 11F06, 11F11 Downloads: Full-text PDF