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Untersuchung Selbergscher Zetafunktionen
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1989 Volume 41 Issue 3 Pages 503-537
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- Published: 1989 Received: May 23, 1988 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) E. W. Barnes, The theory of the G-f unction, Quart. J. of Pure and Appi. Math., 31(1900), 264-314.
2) H. Buchholz, The confluent hypergeometric function, Springer, 1969.
3) U. Christian, Über die Anzahl der Spitzen Siegel'scher Modulgruppen, Abh. Math. Sem Univ Hamburg, 32 (1968), 55-60.
4) U. Christian, Über die analytische Fortsetzung gewisser Poincaréscher Reihen zu elliptischen Modulgruppen, Tohoku Math. J., 40 (1988), 549-590.
5) U. Christian, Über gewisse Poincaré'sche Reihen zu elliptischen Modulgruppen, Manuscripta Math., 59 (1987), 423-440
6) P. Deligne and J. P. Serre, Formes modulaires de poids 1, Ann. Sci. École Norm. Sup., 4e série, 7 (1974), 507-530.
7) I. Efrat, The Selberg trace formula for PSL2 (R)n, Mem. Amer. Math Soc., 65, 359 (1987).
8) I. Efrat, Eisenstein series and Cartan groups, Illinois J. Math., 31 (1987), 428-437.
9) A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions I, II, III, Mc. Graw-Hill.
10) D. Fay, Fourier coefficients of the resolvent for a Fuchsian group, J. Reine Angew. Math., 293/294 (1977), 143-203.
11) J. Fischer, An approach to the Selberg trace formula via the Selberg-zeta-function, Lecture Notes in Math., 1253, Springer, 1987.
12) R. C. Gunning, Lectures on modular forms, Princeton Univ. Press, 1962.
13) D. A Hejhal, The Selberg trace formula for PSL(2, R), I, 548, 1976; II, 1001, 1983, Lecture Notes in Math., Springer.
14) D. A. Hejhal, The Selberg trace formula and the Riemann zeta function, Duke Math J., 43(1976), 441-482.
15) T. Hiramatsu, Eichler classes attached to automorphic forms of dimension -1, Osaka J. Math., 3 (1966), 39-48.
16) T. Hiramatsu, On automorphic forms of weight one I, Mathematics seminar notes, 8 (1980), 173-179.
17) T. Hiramatsu, On automorphic forms of weight one, III. The Selberg eigenspace for discontinuous groups of finite type, preprint.
18) T. Hiramatsu, On some dimension formula for automorphic forms of weight one, I, Nagoya Math. J., 85 (1982), 213-221; II, Nagoya Math. J., 105 (1987), 169-186.
19) T. Hiramatsu, Theory of automorphic forms of weight 1, Adv. Stud. Pure Math., 13 (1988), 503-584.
20) T. Hiramatsu, A formula for the dimension of spaces of cusp forms of weight 1, to appear in Adv. Stud. Pure Math, 15.
21) T. Hiramatsu and S. Akiyama, On some dimension formula for automorphic forms of weight one III, Nagoya Math., J., 111 (1988), 157-163.
22) T. Hiramatsu and Y. Mimura, On automorphic forms of weight one II, Mathematics seminar notes, 9 (1981), 259-267.
23) H. Ishikawa and Y. Tanigawa, The dimension formula of the space of cusp forms of weight one for Γ0(p), Proc. Japan Acad, 63 (1987), 31-34, und preprint.
24) M. Koecher, Zur Theorie der Modulfunktionen n-ten Grades I, Math Z., 59 (1954), 399-416.
25) N. Nielsen, Die Gammafunktion, Chelsea.
26) W. Roelcke, Über die Wellengleichung bei Grenzkreisgruppen erster Art, Sitzungsber. Heidelb. Akad. Wiss., 1956, pp. 161-267.
27) W. Roelcke, Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene, I, Math. Ann., 167 (1966), 292-337, II, Math Ann, 168 (1967), 261-324.
28) A Selberg, Harmonic analysis, Göttingen, 1954.
29) A Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc, 20 (1956),47-87.
30) J. P. Serre, Modular forms of weight one and Galois representations. Algebraic number fields, A Fröhlich (edit), Academic Press, London, 1977.
31) A. B. Venkov, Spectral theory of automorphic functions, the Selberg zeta-function, and some problems of analytic number theory and mathematical physics, RussianMath. Surveys, 34 (1979), 79-153.
32) A. B. Venkov, Spectral theory of automorphic functions, Proc Steklov Inst. Math., 153 (1981), 1-163.
33) M.-F. Vignéras, Examples de sous-groupes discrete non conjugués de PSL (2, R) qui ont même fonction zêta de Selberg, Comptes Rendus, Paris, 287 (1978), 47-49.
34) M -F Vignéras, L'equation functionielle de la fonction zêta de Selberg du groupe modulaire PSL(2, Z), Astérisque, 61 (1979), 235-249
35) E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Univ. Press, 1927.
36) S Akiyama, Selberg trace formula for odd weight, to appear in Proc. Japan Acad
37) U. Christian, Zur Theorie Selbergscher Zetafunktionen, Arch. Math, (to appear).
Right : [1] E. W. Barnes, The theory of the G-f unction, Quart. J. of Pure and Appl. Math., 31 (1900), 264-314.
[2] H. Buchholz, The confluent hypergeometric function, Springer, 1969.
[3] U. Christian, Über die Anzahl der Spitzen Siegel'scher Modulgruppen, Abh. Math. Sem Univ Hamburg, 32 (1968), 55-60.
[4] U. Christian, Über die analytische Fortsetzung gewisser Poincaréscher Reihen zu elliptischen Modulgruppen, Tôhoku Math. J., 40 (1988), 549-590.
[5] U. Christian, Über gewisse Poincaré'sche Reihen zu elliptischen Modulgruppen, Manuscripta Math., 59 (1987), 423-440
[6] P. Deligne and J. P. Serre, Formes modulaires de poids 1, Ann. Sci. École Norm. Sup., 4e série, 7 (1974), 507-530.
[7] I. Efrat, The Selberg trace formula for PSL2 (R)n, Mem. Amer. Math Soc., 65, 359 (1987).
[8] I. Efrat, Eisenstein series and Cartan groups, Illinois J. Math., 31 (1987), 428-437.
[9] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions I, II, III, Mc. Graw-Hill.
[10] D. Fay, Fourier coefficients of the resolvent for a Fuchsian group, J. Reine Angew. Math., 293/294 (1977), 143-203.
[11] J. Fischer, An approach to the Selberg trace formula via the Selberg-zeta-function, Lecture Notes in Math., 1253, Springer, 1987.
[12] R. C. Gunning, Lectures on modular forms, Princeton Univ. Press, 1962.
[13] D. A Hejhal, The Selberg trace formula for PSL(2,R), I, 548, 1976; II, 1001, 1983, Lecture Notes in Math., Springer.
[14] D. A. Hejhal, The Selberg trace formula and the Riemann zeta function, Duke Math J., 43 (1976), 441-482.
[15] T. Hiramatsu, Eichler classes attached to automorphic forms of dimension -1, Osaka J. Math., 3 (1966), 39-48.
[16] T. Hiramatsu, On automorphic forms of weight one I, Mathematics seminar notes, 8 (1980), 173-179.
[17] T. Hiramatsu, On automorphic forms of weight one, III. The Selberg eigenspace for discontinuous groups of finite type, preprint.
[18] T. Hiramatsu, On some dimension formula for automorphic forms of weight one, I, Nagoya Math. J., 85 (1982), 213-221; II, Nagoya Math. J., 105 (1987), 169-186.
[19] T. Hiramatsu, Theory of automorphic forms of weight 1, Adv. Stud. Pure Math., 13 (1988), 503-584.
[20] T. Hiramatsu, A formula for the dimension of spaces of cusp forms of weight 1, to appear in Adv. Stud. Pure Math, 15.
[21] T. Hiramatsu and S. Akiyama, On some dimension formula for automorphic forms of weight one III, Nagoya Math., J., 111 (1988), 157-163.
[22] T. Hiramatsu and Y. Mimura, On automorphic forms of weight one II, Mathematics seminar notes, 9 (1981), 259-267.
[23] H. Ishikawa and Y. Tanigawa, The dimension formula of the space of cusp forms of weight one for Γ0(p), Proc. Japan Acad, 63 (1987), 31-34, und preprint.
[24] M. Koecher, Zur Theorie der Modulfunktionen n-ten Grades I, Math Z., 59 (1954), 399-416.
[25] N. Nielsen, Die Gammafunktion, Chelsea.
[26] W. Roelcke, Über die Wellengleichung bei Grenzkreisgruppen erster Art, Sitzungsber. Heidelb. Akad. Wiss., 1956, pp. 161-267.
[27] W. Roelcke, Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene, I, Math. Ann., 167 (1966), 292-337, II, Math Ann, 168 (1967), 261-324.
[28] A Selberg, Harmonic analysis, Göttingen, 1954.
[29] A Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc, 20 (1956),47-87.
[30] J. P. Serre, Modular forms of weight one and Galois representations. Algebraic number fields, A Fröhlich (edit), Academic Press, London, 1977.
[31] A. B. Venkov, Spectral theory of automorphic functions, the Selberg zeta-function, and some problems of analytic number theory and mathematical physics, Russian Math. Surveys, 34 (1979), 79-153.
[32] A. B. Venkov, Spectral theory of automorphic functions, Proc Steklov Inst. Math., 153 (1981), 1-163.
[33] M. -F. Vignéras, Examples de sous-groupes discrete non conjugués de PSL (2,R) qui ont même fonction zêta de Selberg, Comptes Rendus, Paris, 287 (1978), 47-49.
[34] M -F Vignéras, L'equation functionielle de la fonction zêta de Selberg du groupe modulaire PSL(2,Z), Astérisque, 61 (1979), 235-249
[35] E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Univ. Press, 1927.
[36] S Akiyama, Selberg trace formula for odd weight, to appear in Proc. Japan Acad
[37] U. Christian, Zur Theorie Selbergscher Zetafunktionen, Arch. Math, (to appear).
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