On elliptic analogue of the Hardy sums

키워드

참고문헌 (31)

1. T.M.Apostol, "Modular Functions and Dirichlet Series in Number Theory" (1976), Springer-Verlag
2. A. Bayad, "Applications aux sommes elliptiques d'Apostol-Dedekind-Zagier", C. R. Math.Acad. Sci. Paris, 339(8), pp.529~532 (2004)
3. A. Bayad, "Sommes elliptiques multiples d'Apostol-Dedekind-Zagier", C. R. Math. Acad.Sci. Paris, 339(7), pp.457~462 (2004)
4. B. C. Berndt, "Generalized Dedekind eta-functions and generalized Dedekind sums", Trans. Amer. Math. Soc., 178, pp.495~508 (1973)
5. B. C. Berndt, "Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan", J. Reine Angew. Math., 303, pp.332~365 (1978)
6. B. C. Berndt, "Analytic properties of arithmetic sums arising in the theory of the classical theta functions", SIAM J. Math. Anal., 15(1), pp.143~150 (1984)
7. B. C. Berndt, "Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory", Acta Arith, 28(1), pp.23~68 (1975)
8. B. C. Berndt, "Explicit evaluations and reciprocity theorems for nite trigonometric sums", Adv. in Appl. Math., 29(3), pp.358~385 (2002)
9. D. Bertrand, "Theta functions and transcendence", Ramanujan J., 1(4), pp.339~350 (1997)
10. M. Can, "Generalized Hardy-Berndt sums", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 9(1), pp.19~38 (2006), 장전수학회
11. U. Dieter, "Cotangent sums, a further generalization of Dedekind sums", J. Number The-ory, 18(3), pp.289~305 (1984)
12. S. Egami, "An elliptic analogue of the multiple Dedekind sums", Compositio Math, 99(1), pp.99~103 (1995)
13. M. I. Knoop, "Modular Functions in Analytic Number Theory" (1970), Markham Publishing Company
14. N. Koblitz, "Introduction to Elliptic Curves and Modular Forms" (1993), Springer-Verlag
15. V. Kurt, "On Dedekind sums", Indian J. Pure Appl. Math, 21(10), pp.893~896 (1990)
16. J. Lewittes, "Analytic continuation of the series ∑(m+nz)−s", Trans. Amer. Math. Soc, 159, pp.505~509 (1971)
17. J. Lewittes, "Trans. Amer. Math. Soc.Analytic continuation of Eisenstein series", Trans. Amer. Math. Soc, 171, pp.469~490 (1972)
18. S. J. Patterson, "An Introduction to the Theory of the Riemann Zeta-Function" (1988), Cam-bridge University Press
19. M. R. Pettet, "Three-term relations for Hardy sums", J. Num-ber Theory, 25(3), pp.328~339 (1987)
20. H. Rademacher, "Zur Theorie der Modulfunktionen", J. Reine Angew. Math., 167, pp.312~336 (1932)
21. H.Rademacher, "Topics in Analytic Number Theory" (1988), Springer-Verlag
22. R. A. Rankin, "Elementary proofs of relations between Eisenstein series", Proc. Roy. Soc.Edinburgh Sect. A, 76(2), pp.107~117 (1976)
23. B. Schoneneberg, "Zur Theorie der verallgemeinerten Dedekindschen Modulfunktionen", Nachr. Akad. Wiss. Gottingen Math.-Phys. Kl. II, pp.119~128 (1969)
24. Y. Simsek, "Theorems on three-term relations for Hardy sums", Turkish J. Math, 22(2), pp.153~162 (1998)
25. Y. Simsek, "Relations between theta-functions Hardy sums Eisenstein and Lambert series in the transformation formula of logg;h(z)", J. Number Theory, 99(2), pp.338~360 (2003)
26. Y. Simsek, "On Weierstrass }(z) function Hardy sums and Eisenstein series", Proc. Jang-jeon Math. Soc., 7(2), pp.99~108 (2004)
27. Y. Simsek, "Generalized Dedekind sums associated with the Abel sum and the Eisenstein and Lambert series", Adv. Stud. Contemp. Math., 9(2), pp.125~137 (2004)
28. Y. Simsek, "Transformation of four Titchmarsh-type in nite integrals and generalized Dedekind sums associated with Lambert series", Adv. Stud. Contemp. Math.(Kyungshang), 9(2), pp.195~202 (2004)
29. R. Sitaramachandrarao, "Dedekind and Hardy sums", Acta Arith, 48, pp.325~340 (1978)
30. M. Waldschmidt, "From Number Theory to Physics" (1995), Springer-Verlag
31. D. Zagier, "Higher dimensional Dedekind sums", Math. Ann., 202, pp.149~172 (1973)

관련 논문AI추천