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For a positive integer $k$ and an arbitrary integer $h$, the
classical Dedekind sums $s(h, k)$ is defined by
<수식>
where
<수식>J. B. Conrey et al proved that
<수식>
For m≥2, C. Jia reduced the error terms to O(k^{2m-1}). While for m=1, W. Zhang showed
<수식>
In this paper we give some formulae on the mean value of the
Dedekind sums and and Hardy sums, and generalize the above results.
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참고문헌 (22)
참고문헌 신청
B. C. Berndt / 1974 / A new proof of the reciprocity theorem for Dedekind sums / Elem. Math. 29 : 93 ~ 94
B. C. Berndt / 1976 / Dedekind sums and a paper of G. H. Hardy / J. London Math. Soc. 13 (1) : 129 ~ 137
B. C. Berndt / 1977 / Reciprocity theorems for Dedekind sums and generalizations / Advances in Math 238 (33) : 285 ~ 316
B. C. Berndt / 1978 / Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan / J. Reine Angew. Math. 303 : 332 ~ 365
B. C. Berndt / 1984 / Analytic properties of arithmetic sums arising in the theory of the classical theta functions / SIAM J. Math. Anal. 15 (1) : 143 ~ 150
B. C. Berndt / 1976 / Dedekind sums and a paper of G. H. Hardy / J. London Math. Soc. 13 (1) : 129 ~ 137
B. C. Berndt / 1977 / Reciprocity theorems for Dedekind sums and generalizations / Advances in Math 238 (33) : 285 ~ 316
B. C. Berndt / 1978 / Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan / J. Reine Angew. Math. 303 : 332 ~ 365
B. C. Berndt / 1984 / Analytic properties of arithmetic sums arising in the theory of the classical theta functions / SIAM J. Math. Anal. 15 (1) : 143 ~ 150
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