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On Periods of Meromorphic Eichler Integrals

Published online by Cambridge University Press:  22 January 2016

Hiroki Sato
Hiroki Sato*
Affiliation:
Department of Mathematics, Shizuoka University
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In this paper we treat cohomology groups H1(G, C2q-1, M) of meromorphic Eichler integrals for a finitely generated Fuchsian group G of the first kind. According to L. V. Ahlfors [2] and L. Bers [4], H1(G, C2q-1, M) is the space of periods of meromorphic Eichler integrals for G. In the previous paper [8], we had period relations and inequalities of holomorphic Eichler integrals for a certain Kleinian groups.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 57 , June 1975 , pp. 1 - 26
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] Ahlfors, L. V., Finitely generated Kleinian groups, Amer. J. Math., 86 (1964), 413–429 and 87 (1965), 759. MR 29 #4890; MR 31 #4906.Google Scholar
[2] Ahlfors, L. V., The structure of a finitely generated Kleinian group, Acta Math., 122 (1969), 1–17. MR 38 #6063.Google Scholar
[3] Bers, L., Inequalities for finitely generated Kleinian groups, J. Anal. Math., 18 (1967), 23–41. MR 37 #5358.CrossRefGoogle Scholar
[4] Bers, L., Eichler integrals with singularities. Acta Math., 127 (1971), 11–22. MR 42 #6224.Google Scholar
[5] Eichler, M., Eine Verallgemeinerung der Abelschen Integrale, Math. Z., 67 (1957), 267–298. MR 19, 740.CrossRefGoogle Scholar
[6] Kra, I., On cohomology of Kleinian groups, Ann. of Math., 89 (1969), 533–556. MR 41 #8656a.Google Scholar
[7] Kra, I., On cohomology of Kleinian groups, II, Ann. of Math., 90 (1969), 575–589. MR 41 #8656b.Google Scholar
[8] Sato, H., The periods of Eichler integrals for Kleinian groups, Trans. Amer. Math. Soc., 184 (1973), 439–456.Google Scholar
[9] Shimura, G., Sur les intégrales attachées aux formes automorphes, Jour. Math. Soc. of Japan, 11 (1959), 291–311. MR 22 #11126.Google Scholar