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Volumn 89, Issue 1, 2001, Pages 1-13

A Sum Analogous to the Dedekind Sum and its Mean Value Formula

Author keywords

Asymptotic formula; Dedekind sums; Distribution of the mean value

Indexed keywords


EID: 0041738893     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jnth.2000.2624     Document Type: Article
Times cited : (10)

References (12)
  • 3
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    • Berndt B. C. Analytic eisenstein series, theta-function, and series relations in the spirit of Ramanujan. J. Reine Angew. Math. 303/304:1978;332-365.
    • (1978) J. Reine Angew. Math. , vol.303-304 , pp. 332-365
    • Berndt, B.C.1
  • 4
    • 84972493817 scopus 로고
    • The reciprocity theorem of Dedekind Sums
    • Carlitz L. The reciprocity theorem of Dedekind Sums. Pacific J. Math. 3:1953;513-522.
    • (1953) Pacific J. Math. , vol.3 , pp. 513-522
    • Carlitz, L.1
  • 7
    • 0002473640 scopus 로고
    • On the transformation of log η(τ)
    • Rademacher H. On the transformation of log η(τ). J. Indian. Math. Soc. 19:1955;25-30.
    • (1955) J. Indian. Math. Soc. , vol.19 , pp. 25-30
    • Rademacher, H.1
  • 8
    • 84972530033 scopus 로고
    • Generalization of the reciprocity formula for Dedekind Sums
    • Rademacher H. Generalization of the reciprocity formula for Dedekind Sums. Duke J. Math. 21:1954;391-397.
    • (1954) Duke J. Math. , vol.21 , pp. 391-397
    • Rademacher, H.1
  • 9
    • 0002475887 scopus 로고
    • On certain series of discontinuous functions connected with the modular functions
    • Hardy G. H. On certain series of discontinuous functions connected with the modular functions. Quart. J. Math. 36:1905;93-123.
    • (1905) Quart. J. Math. , vol.36 , pp. 93-123
    • Hardy, G.H.1
  • 10
    • 0002378122 scopus 로고
    • An exact formula for an average of L-series
    • Walum H. An exact formula for an average of L-series. Illinois J. Math. 26:1982;1-3.
    • (1982) Illinois J. Math. , vol.26 , pp. 1-3
    • Walum, H.1
  • 11
    • 85009921552 scopus 로고    scopus 로고
    • On the mean values of Dedekind Sums
    • Zhang W. On the mean values of Dedekind Sums. J. Theor. Nombres. 8:1996;429-442.
    • (1996) J. Theor. Nombres , vol.8 , pp. 429-442
    • Zhang, W.1
  • 12
    • 0034146977 scopus 로고    scopus 로고
    • A note on the mean square value of the Dedekind sums
    • Zhang W. A note on the mean square value of the Dedekind sums. Acta Math. Hungar. 86:2000;275-289.
    • (2000) Acta Math. Hungar. , vol.86 , pp. 275-289
    • Zhang, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.