Open Access
March 2001 On certain Cohomology Set for $\Gamma _0(N)$
Takashi Ono
Proc. Japan Acad. Ser. A Math. Sci. 77(3): 39-41 (March 2001). DOI: 10.3792/pjaa.77.39


Let $G = \Gamma_0(N)$, $N \not\equiv 3 \pmod{4}$ and $g$ be the group generated by the involution $z \mapsto -1/Nz$ of the upper half plane. We determine the cohomology set $H^1(g,G)$ in terms of the class number of quadratic forms of discriminant $-4N$.


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Takashi Ono. "On certain Cohomology Set for $\Gamma _0(N)$." Proc. Japan Acad. Ser. A Math. Sci. 77 (3) 39 - 41, March 2001.


Published: March 2001
First available in Project Euclid: 23 May 2006

zbMATH: 1039.11033
MathSciNet: MR1822151
Digital Object Identifier: 10.3792/pjaa.77.39

Primary: 11F75

Keywords: binary quadratic forms , class number of orders , cohomology sets , Congruence subgroups of level $N$ , the involution

Rights: Copyright © 2001 The Japan Academy

Vol.77 • No. 3 • March 2001
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