Arithmetic of the modular function j 1 , 4

Chang Heon Kim; Ja Kyung Koo

Acta Arithmetica (1998)

  • Volume: 84, Issue: 2, page 129-143
  • ISSN: 0065-1036

Abstract

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We find a generator j 1 , 4 of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator N ( j 1 , 4 ) which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.

How to cite

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Chang Heon Kim, and Ja Kyung Koo. "Arithmetic of the modular function $j_{1,4}$." Acta Arithmetica 84.2 (1998): 129-143. <http://eudml.org/doc/207138>.

@article{ChangHeonKim1998,
abstract = {We find a generator $j_\{1,4\}$ of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator $N(j_\{1,4\})$ which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.},
author = {Chang Heon Kim, Ja Kyung Koo},
journal = {Acta Arithmetica},
keywords = {modular function; normalized generator of a function field; moonshine; complex multiplication; class fields over imaginary quadratic fields},
language = {eng},
number = {2},
pages = {129-143},
title = {Arithmetic of the modular function $j_\{1,4\}$},
url = {http://eudml.org/doc/207138},
volume = {84},
year = {1998},
}

TY - JOUR
AU - Chang Heon Kim
AU - Ja Kyung Koo
TI - Arithmetic of the modular function $j_{1,4}$
JO - Acta Arithmetica
PY - 1998
VL - 84
IS - 2
SP - 129
EP - 143
AB - We find a generator $j_{1,4}$ of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator $N(j_{1,4})$ which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.
LA - eng
KW - modular function; normalized generator of a function field; moonshine; complex multiplication; class fields over imaginary quadratic fields
UR - http://eudml.org/doc/207138
ER -

References

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  15. [15] Norton, S.P., More on moonshine, in: Computational Group Theory, Academic Press, London, 1984, 185-195. 
  16. [16] Rankin, R., Modular Forms and Functions, Cambridge Univ. Press, Cambridge, 1977. 
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  20. [20] Thompson, J.G., Some numerology between the Fischer-Griess monster and the elliptic modular function, Bull. London Math. Soc. 11 (1979), 352-353. Zbl0425.20016

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