Properties of certain integer-valued analogues of Dedekind sums

• Autorzy: Jeffrey L. Meyer
• Języki publikacji: EN

Kategorie tematyczne

• 11F20: Dedekind eta function, Dedekind sums
• 11A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 82
• Numer: 3
• Strony: 229-242

Daty

wydano

1997

otrzymano

1996-07-09

poprawiono

1997-04-11

Twórcy

autor

Jeffrey L. Meyer

• Department of Mathematics, Syracuse University, Syracuse, New York 13244-1150, U.S.A.

Bibliografia

• [1] T. Asai, Some arithmetic on Dedekind sums, J. Math. Soc. Japan 38 (1986), 163-172.
• [2] B. C. Berndt, Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan, J. Reine Angew. Math. 303/304 (1978), 332-365.
• [3] R. Dedekind, Erläuterungen zu zwei Fragmenten von Riemann, in: Riemann's Gesammelte Math. Werke, 2nd ed., 1882, 466-472.
• [4] W. Duke, J. B. Friedlander and H. Iwaniec, Equidistribution of roots of a quadratic congruence to prime moduli, Ann. of Math. 141 (1995), 423-441.
• [5] L. A. Goldberg, Transformations of theta-functions and analogues of Dedekind sums, thesis, Univ. of Illinois, Urbana, 1981.
• [6] G. H. Hardy, On certain series of discontinuous functions connected with the modular functions, Quart. J. Math. Oxford 36 (1905), 93-123.
• [7] G. H. Hardy, Collected Papers, Vol. IV, Clarendon Press, Oxford, 1969.
• [8] D. Hickerson, Continued fractions and density results for Dedekind sums, J. Reine Angew. Math. 290 (1977), 113-116.
• [9] J. L. Meyer, Analogues of Dedekind sums, thesis, Univ. of Illinois, Urbana, 1997.
• [10] I. Niven, H. Zuckerman and H. Montgomery, An Introduction to the Theory of Numbers, 5th ed., Wiley, 1991.
• [11] L. Pinzur, On a question of Rademacher concerning Dedekind sums, Proc. Amer. Math. Soc. 61 (1976), 11-15.
• [12] H. Rademacher, Zur Theorie der Dedekindschen Summen, Math. Z. 63 (1956), 445-463.
• [13] H. Rademacher, Questions 99 and 100, in: Proc. 1963 Number Theory Conference, Univ. of Colorado, Boulder, Colo., 1963, 112.
• [14] K. Rosen, On the sign of some Dedekind sums, J. Number Theory 9 (1977), 209-212.
• [15] R. Sitaramachandrarao, Dedekind and Hardy sums, Acta Arith. 48 (1987), 325-340.