Some new results on the Eichler cohomology of automorphic forms

Knopp, Marvin I.

doi:10.1090/S0002-9904-1974-13520-2

Author: Marvin I. Knopp
Journal: Bull. Amer. Math. Soc. 80 (1974), 607-632
MSC (1970): Primary 30A58; Secondary 10D15, 20H10
DOI: https://doi.org/10.1090/S0002-9904-1974-13520-2
MathSciNet review: 0344454
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G. Bol, Invarianten linearer differentialgleichungen, Abh. Math. Sem. Univ. Hamburg 16 (1949), no. nos. 3-4, 1–28 (German). MR 33411, DOI https://doi.org/10.1007/BF03343515
M. Eichler, Eine Verallgemeinerung der Abelschen Integrale, Math. Z. 67 (1957), 267–298 (German). MR 89928, DOI https://doi.org/10.1007/BF01258863
M. Eichler, Grenzkreisgruppen und kettenbruchartige Algorithmen, Acta Arith. 11 (1965), 169–180 (German). MR 228436, DOI https://doi.org/10.4064/aa-11-2-169-180

4. M. Eichler, Lectures on modular correspondences, Tata Institute of Fundamental Research, Bombay, 1955/56.

R. C. Gunning, The Eichler cohomology groups and automorphic forms, Trans. Amer. Math. Soc. 100 (1961), 44–62. MR 140126, DOI https://doi.org/10.1090/S0002-9947-1961-0140126-3
Sufian Y. Husseini and Marvin I. Knopp, Eichler cohomology and automorphic forms, Illinois J. Math. 15 (1971), 565–577. MR 285733
Marvin Isadore Knopp, Construction of automorphic forms on $H$-groups and supplementary Fourier series, Trans. Amer. Math. Soc. 103 (1962), 168–188. MR 136735, DOI https://doi.org/10.1090/S0002-9947-1962-0136735-9
Marvin I. Knopp, Notes on automorphic functions: An entire automorphic form of positive dimension is zero, J. Res. Nat. Bur. Standards Sect. B 71B (1967), 167–169. MR 237783
M. I. Knopp, J. Lehner, and M. Newman, A bounded automorphic form of dimension zero is constant, Duke Math. J. 32 (1965), 457–460. MR 196076
Irwin Kra, Automorphic forms and Kleinian groups, W. A. Benjamin, Inc., Reading, Mass., 1972. Mathematics Lecture Note Series. MR 0357775
Irwin Kra, On cohomology of kleinian groups, Ann. of Math. (2) 89 (1969), 533–556. MR 264059, DOI https://doi.org/10.2307/1970650
Irwin Kra, On cohomology of kleinian groups, Ann. of Math. (2) 89 (1969), 533–556. MR 264059, DOI https://doi.org/10.2307/1970650
Joseph Lehner, Automorphic integrals with preassigned period polynomials and the Eichler cohomology, Computers in number theory (Proc. Sci. Res. Council Atlas Sympos. No. 2, Oxford, 1969) Academic Press, London, 1971, pp. 49–56. MR 0316387
Joseph Lehner, Automorphic integrals with preassigned periods, J. Res. Nat. Bur. Standards Sect. B 73B (1969), 153–161. MR 248085
Joseph Lehner, Discontinuous groups and automorphic functions, Mathematical Surveys, No. VIII, American Mathematical Society, Providence, R.I., 1964. MR 0164033
Joseph Lehner, The Eichler cohomology of a Kleinian group, Math. Ann. 192 (1971), 125–143. MR 294636, DOI https://doi.org/10.1007/BF02052757
Joseph Lehner, A short course in automorphic functions, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1966. MR 0201637

18. D. P. Niebur, Automorphic integrals of arbitrary positive dimension and Poincaré series, Doctoral Dissertation, University of Wisconsin, Madison, Wis., 1968.

Hans Petersson, Automorphe Formen als metrische Invarianten. I. Automorphe Formen, metrische Verknüpfung, Eigenfunktionen linearer Funktionale, Math. Nachr. 1 (1948), 158–212 (German). MR 27860, DOI https://doi.org/10.1002/mana.19480010203
Hans Petersson, Automorphe Formen als metrische Invarianten. II. Multiplikative Differentiale als Grenzwerte metrischer Invarianten von stetig veränderlicher reeller Dimension, Math. Nachr. 1 (1948), 218–257 (German). MR 28964, DOI https://doi.org/10.1002/mana.19480010203
Hans Petersson, Explizite Konstruktion der automorphen Orthogonalfunktionen in den multiplikativen Differentialklassen, Math. Nachr. 16 (1957), 343–368 (German). MR 98181, DOI https://doi.org/10.1002/mana.19570160508
Hans Petersson, Konstruktion der Modulformen und der zu gewissen Grenzkreisgruppen gehörigen automorphen Formen von positiver reeller Dimension und die vollständige Bestimmung ihrer Fourierkoeffizienten, S.-B. Heidelberger Akad. Wiss. Math.-Nat. Kl. 1950 (1950), 417–494 (German). MR 0041172
Hans Petersson, Zur analytischen Theorie der Grenzkreisgruppen, Math. Ann. 115 (1938), no. 1, 175–204 (German). MR 1513184, DOI https://doi.org/10.1007/BF01448938