Dedekind sums for Hecke groups
Acta Arithmetica (1995)
- Volume: 71, Issue: 1, page 11-46
- ISSN: 0065-1036
Access Full Article
topHow to cite
topRoelof W. Bruggeman. "Dedekind sums for Hecke groups." Acta Arithmetica 71.1 (1995): 11-46. <http://eudml.org/doc/206757>.
@article{RoelofW1995,
author = {Roelof W. Bruggeman},
journal = {Acta Arithmetica},
keywords = {reciprocity relation; distribution result; automorphic forms; Eisenstein series; generalized Dedekind sums; Hecke groups; Poincaré series},
language = {eng},
number = {1},
pages = {11-46},
title = {Dedekind sums for Hecke groups},
url = {http://eudml.org/doc/206757},
volume = {71},
year = {1995},
}
TY - JOUR
AU - Roelof W. Bruggeman
TI - Dedekind sums for Hecke groups
JO - Acta Arithmetica
PY - 1995
VL - 71
IS - 1
SP - 11
EP - 46
LA - eng
KW - reciprocity relation; distribution result; automorphic forms; Eisenstein series; generalized Dedekind sums; Hecke groups; Poincaré series
UR - http://eudml.org/doc/206757
ER -
References
top- [1] M. Atiyah, The logarithm of the Dedekind η-function, Math. Ann. 278 (1987), 335-380. Zbl0648.58035
- [2] R. W. Bruggeman, Modular forms of varying weight. I, Math. Z. 190 (1985), 477-495. Zbl0553.10021
- [3] R. W. Bruggeman, Modular forms of varying weight. II, Math. Z. 192 (1986), 297-328. Zbl0569.10011
- [4] R. W. Bruggeman, Modular forms of varying weight. III, J. Reine Angew. Math. 371 (1986), 144-190. Zbl0588.10021
- [5] R. W. Bruggeman, Eisenstein series and the distribution of Dedekind sums, Math. Z. 202 (1989), 181-198. Zbl0655.10026
- [6] R. W. Bruggeman, On the distribution of Dedekind sums, in: Proc. Internat. Conf. Automorphic Functions and their Applications, Khabarovsk, 1988, N. Kuznetsov and V. Bykovsky (eds.), 82-89. Zbl0742.11024
- [7] R. W. Bruggeman, Dedekind sums and Fourier coefficients of modular forms, J. Number Theory 36 (1990), 289-321. Zbl0723.11018
- [8] R. W. Bruggeman, On the distribution of Dedekind sums, in: Contemp. Math. 166, Amer. Math. Soc., 1994, 197-210. Zbl0810.11025
- [9] R. W. Bruggeman, Families of Automorphic Forms, Monographs Math. 88, Birkhäuser, 1994. Zbl0821.11029
- [10] R. Dedekind, Erläuterungen zu den Fragmenten XXVIII, in: B. Riemann, Gesammelte mathematische Werke und wissenschaftlicher Nachlass, H. Weber (ed.); reprint, Dover Publ., 1953, 466-478.
- [11] L. J. Goldstein, Dedekind sums for a Fuchsian group, I, Nagoya Math. J. 50 (1973), 21-47. Zbl0267.10039
- [12] L. J. Goldstein, Errata for Dedekind sums for a Fuchsian group, I, Nagoya Math. J. 53 (1974), 235-237. Zbl0282.10017
- [13] L. J. Goldstein, Dedekind sums for a Fuchsian group, II, Nagoya Math. J. 53 (1974), 171-187. Zbl0289.10018
- [14] E. Hecke, Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung, Math. Ann. 112 (1936), 664-699. Zbl0014.01601
- [15] E. Hecke, Dirichlet Series, Modular Functions and Quadratic Forms, lecture notes by H. Serbin, Institute of Adv. Study, Princeton, 1938.
- [16] D. A. Hejhal, The Selberg Trace Formula for PSL(2,ℝ), Vol. 2, Lecture Notes in Math. 1001, Springer, 1983.
- [17] S. Lang, Algebraic Number Theory, Addison-Wesley, 1970. Zbl0211.38404
- [18] A. Leutbecher, Über die Heckeschen Gruppen G(λ), I, Abh. Math. Sem. Univ. Hamburg 31 (1967), 199-205. Zbl0161.27601
- [19] H. Maaß, Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 121 (1949), 141-183. Zbl0033.11702
- [20] H. Maaß, Modular Functions of One Complex Variable, Tata Institute, Bombay, 1964; 2nd ed., Springer, 1983. Zbl0254.10018
- [21] R. Matthes, The Eisenstein family for the modular group along closed geodesics, Math. Z., to appear. Zbl0868.11023
- [22] H. Neunhöffer, Über die analytische Fortsetzung von Poincaréreihen, Sitzungsber. Heidelb. Akad. Wiss. Math.-Natur. Kl., 2. Abhandlung, 1973, 33-90.
- [23] H. Petersson, Zur analytischen Theorie der Grenzkreisgruppen, I, Math. Ann.115 (1937), 23-67.
- [24] H. Rademacher and E. Grosswald, Dedekind Sums, Math. Assoc. Amer., 1972.
- [25] L. J. Slater, Confluent Hypergeometric Functions, Cambridge University Press, 1960. Zbl0086.27502
- [26] I. Vardi, Dedekind sums have a limiting distribution, Duke Math. J. 69, Int. Math. Research Notices (1993), 1-12. Zbl0785.11028
- [27] D. V. Widder, The Laplace Transform, Princeton University Press, 1946. Zbl0060.24801
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.