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      On elliptic analogue of the Hardy sums

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      https://www.riss.kr/link?id=A103365818

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      다국어 초록 (Multilingual Abstract)

      Main purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to elliptic analogue of the Hardy sums, are given.

      Main purpose of this paper is to define an elliptic analogue of the
      Hardy sums. Some results, which are related to elliptic analogue of
      the Hardy sums, are given.

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      다국어 초록 (Multilingual Abstract)

      Main purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to elliptic analogue of the Hardy sums, are given.

      Main purpose of this paper is to define an elliptic analogue of the
      Hardy sums. Some results, which are related to elliptic analogue of
      the Hardy sums, are given.

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      참고문헌 (Reference)

      1 B. Schoneneberg, "Zur Theorie der verallgemeinerten Dedekindschen Modulfunktionen" 119-128, 1969

      2 H. Rademacher, "Zur Theorie der Modulfunktionen" 167 : 312-336, 1932

      3 Y. Simsek, "Transformation of four Titchmarsh-type in nite integrals and generalized Dedekind sums associated with Lambert series" 9 (9): 195-202, 2004

      4 J. Lewittes, "Trans. Amer. Math. Soc.Analytic continuation of Eisenstein series" 171 : 469-490, 1972

      5 H.Rademacher, "Topics in Analytic Number Theory" Springer-Verlag 1988

      6 M. R. Pettet, "Three-term relations for Hardy sums" 25 (25): 328-339, 1987

      7 D. Bertrand, "Theta functions and transcendence" 1 (1): 339-350, 1997

      8 Y. Simsek, "Theorems on three-term relations for Hardy sums" 22 (22): 153-162, 1998

      9 A. Bayad, "Sommes elliptiques multiples d'Apostol-Dedekind-Zagier" 339 (339): 457-462, 2004

      10 Y. Simsek, "Relations between theta-functions Hardy sums Eisenstein and Lambert series in the transformation formula of logg;h(z)" 99 (99): 338-360, 2003

      1 B. Schoneneberg, "Zur Theorie der verallgemeinerten Dedekindschen Modulfunktionen" 119-128, 1969

      2 H. Rademacher, "Zur Theorie der Modulfunktionen" 167 : 312-336, 1932

      3 Y. Simsek, "Transformation of four Titchmarsh-type in nite integrals and generalized Dedekind sums associated with Lambert series" 9 (9): 195-202, 2004

      4 J. Lewittes, "Trans. Amer. Math. Soc.Analytic continuation of Eisenstein series" 171 : 469-490, 1972

      5 H.Rademacher, "Topics in Analytic Number Theory" Springer-Verlag 1988

      6 M. R. Pettet, "Three-term relations for Hardy sums" 25 (25): 328-339, 1987

      7 D. Bertrand, "Theta functions and transcendence" 1 (1): 339-350, 1997

      8 Y. Simsek, "Theorems on three-term relations for Hardy sums" 22 (22): 153-162, 1998

      9 A. Bayad, "Sommes elliptiques multiples d'Apostol-Dedekind-Zagier" 339 (339): 457-462, 2004

      10 Y. Simsek, "Relations between theta-functions Hardy sums Eisenstein and Lambert series in the transformation formula of logg;h(z)" 99 (99): 338-360, 2003

      11 B. C. Berndt, "Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory" 28 (28): 23-68, 1975

      12 Y. Simsek, "On Weierstrass }(z) function Hardy sums and Eisenstein series" 7 (7): 99-108, 2004

      13 V. Kurt, "On Dedekind sums" 21 (21): 893-896, 1990

      14 M. I. Knoop, "Modular Functions in Analytic Number Theory" Markham Publishing Company 1970

      15 T.M.Apostol, "Modular Functions and Dirichlet Series in Number Theory" Springer-Verlag 1976

      16 N. Koblitz, "Introduction to Elliptic Curves and Modular Forms" Springer-Verlag 1993

      17 D. Zagier, "Higher dimensional Dedekind sums" 202 : 149-172, 1973

      18 M. Can, "Generalized Hardy-Berndt sums" 장전수학회 9 (9): 19-38, 2006

      19 Y. Simsek, "Generalized Dedekind sums associated with the Abel sum and the Eisenstein and Lambert series" 9 (9): 125-137, 2004

      20 B. C. Berndt, "Generalized Dedekind eta-functions and generalized Dedekind sums" 178 : 495-508, 1973

      21 M. Waldschmidt, "From Number Theory to Physics" Springer-Verlag 1995

      22 B. C. Berndt, "Explicit evaluations and reciprocity theorems for nite trigonometric sums" 29 (29): 358-385, 2002

      23 R. A. Rankin, "Elementary proofs of relations between Eisenstein series" 76 (76): 107-117, 1976

      24 R. Sitaramachandrarao, "Dedekind and Hardy sums" 48 : 325-340, 1978

      25 U. Dieter, "Cotangent sums, a further generalization of Dedekind sums" 18 (18): 289-305, 1984

      26 A. Bayad, "Applications aux sommes elliptiques d'Apostol-Dedekind-Zagier" 339 (339): 529-532, 2004

      27 B. C. Berndt, "Analytic properties of arithmetic sums arising in the theory of the classical theta functions" 15 (15): 143-150, 1984

      28 J. Lewittes, "Analytic continuation of the series ∑(m+nz)−s" 159 : 505-509, 1971

      29 B. C. Berndt, "Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan" 303 : 332-365, 1978

      30 S. Egami, "An elliptic analogue of the multiple Dedekind sums" 99 (99): 99-103, 1995

      31 S. J. Patterson, "An Introduction to the Theory of the Riemann Zeta-Function" Cam-bridge University Press 1988

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      2020-01-01 평가 등재학술지 유지 (해외등재 학술지 평가) KCI등재
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      2008-01-01 평가 등재학술지 유지 (등재유지) KCI등재
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      1999-01-01 평가 등재후보학술지 선정 (신규평가) KCI등재후보
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      기준연도 WOS-KCI 통합IF(2년) KCIF(2년) KCIF(3년)
      2016 0.35 0.1 0.27
      KCIF(4년) KCIF(5년) 중심성지수(3년) 즉시성지수
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