The cuspidal class number formula for certain quotient curves of the modular curve $X_{0}(M)$ by Atkin-Lehner involutions
TAKAGI, Toshikazu
J. Math. Soc. Japan, Tome 62 (2010) no. 1, p. 13-47 / Harvested from Project Euclid
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We calculate the cuspidal class number of a certain quotient curve of the modular curve $X_{0}(M)$ with $M$ square-free. For each factor $r$ of $M$ , let $w_{r}$ denote the Atkin-Lehner type involution of $X_{0}(M)$ . Let $M_{0}$ be a divisor of $M$ , and $W_{0}$ the subgroup of the automorphism group of $X_{0}(M)$ consisting of all $w_{r}$ with $r$ dividing $M_{0}$ . Our object is the quotient of $X_{0}(M)$ by $W_{0}$ . In this paper, we consider the case where $M$ is odd.
Publié le : 2010-01-15
Classification:  modular curve,  modular unit,  cuspidal class number,  11F03 
@article{1265380423,
     author = {TAKAGI, Toshikazu},
     title = {The cuspidal class number formula for certain quotient curves of the modular curve $X\_{0}(M)$ by Atkin-Lehner involutions},
     journal = {J. Math. Soc. Japan},
     volume = {62},
     number = {1},
     year = {2010},
     pages = { 13-47},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1265380423}
}

TAKAGI, Toshikazu. The cuspidal class number formula for certain quotient curves of the modular curve $X_{0}(M)$ by Atkin-Lehner involutions. J. Math. Soc. Japan, Tome 62 (2010) no. 1, pp.  13-47. http://gdmltest.u-ga.fr/item/1265380423/