## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### On certain cohomology sets attached to Riemann surfaces

Takashi Ono

#### Abstract

Let $G$ be the principal congruence subgroup of level $N \geq 3$ and $g$ be the group generated by the involution $z \mapsto -1/z$ of the upper half plane. We shall determine the cardinality of the (first) cohomology set $H(g,G)$ in terms of the binary form $x^2 + y^2 \mod N$.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 76, Number 7 (2000), 116-117.

Dates
First available in Project Euclid: 23 May 2006

https://projecteuclid.org/euclid.pja/1148393471

Digital Object Identifier
doi:10.3792/pjaa.76.116

Mathematical Reviews number (MathSciNet)
MR1785637

Zentralblatt MATH identifier
0967.11020

Subjects
Primary: 11F75: Cohomology of arithmetic groups

#### Citation

Ono, Takashi. On certain cohomology sets attached to Riemann surfaces. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 7, 116--117. doi:10.3792/pjaa.76.116. https://projecteuclid.org/euclid.pja/1148393471