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Title

Dedekind sums for Hecke groups

Authors 1

Affiliations

  1. Mathematisch Instituut, Universiteit Utrecht, Postbus 80.010, 3508 Ta Utrecht, The Netherlands

Bibliography

  1. M. Atiyah, The logarithm of the Dedekind η-function, Math. Ann. 278 (1987), 335-380.
  2. R. W. Bruggeman, Modular forms of varying weight. I, Math. Z. 190 (1985), 477-495.
  3. R. W. Bruggeman, Modular forms of varying weight. II, Math. Z. 192 (1986), 297-328.
  4. R. W. Bruggeman, Modular forms of varying weight. III, J. Reine Angew. Math. 371 (1986), 144-190.
  5. R. W. Bruggeman, Eisenstein series and the distribution of Dedekind sums, Math. Z. 202 (1989), 181-198.
  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.
  7. R. W. Bruggeman, Dedekind sums and Fourier coefficients of modular forms, J. Number Theory 36 (1990), 289-321.
  8. R. W. Bruggeman, On the distribution of Dedekind sums, in: Contemp. Math. 166, Amer. Math. Soc., 1994, 197-210.
  9. R. W. Bruggeman, Families of Automorphic Forms, Monographs Math. 88, Birkhäuser, 1994.
  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.
  12. L. J. Goldstein, Errata for Dedekind sums for a Fuchsian group, I, Nagoya Math. J. 53 (1974), 235-237.
  13. L. J. Goldstein, Dedekind sums for a Fuchsian group, II, Nagoya Math. J. 53 (1974), 171-187.
  14. E. Hecke, Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung, Math. Ann. 112 (1936), 664-699.
  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.
  18. A. Leutbecher, Über die Heckeschen Gruppen G(λ), I, Abh. Math. Sem. Univ. Hamburg 31 (1967), 199-205.
  19. H. Maaß, Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 121 (1949), 141-183.
  20. H. Maaß, Modular Functions of One Complex Variable, Tata Institute, Bombay, 1964; 2nd ed., Springer, 1983.
  21. R. Matthes, The Eisenstein family for the modular group along closed geodesics, Math. Z., to appear.
  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.
  26. I. Vardi, Dedekind sums have a limiting distribution, Duke Math. J. 69, Int. Math. Research Notices (1993), 1-12.
  27. D. V. Widder, The Laplace Transform, Princeton University Press, 1946.
Acta Arithmetica
1995/71/1
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Pages:
11-46
Main language of publication
English
Received
1993-11-23
Published
1995
Exact and natural sciences