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Analytic continuation of generalized non-holomorphic Eisenstein series
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B. C. Berndt computed the Fourier series of a class of generalized Eisenstein series, which gives an analytic continuation to the generalized Eisenstein series. In this paper, continuing his work, we consider generalized non-holomorphic Eisenstein series and give an analytic continuation to the s-plane.
Abstract
B. C. Berndt computed the Fourier series of a class of generalized Eisenstein series, which gives an analytic continuation to the generalized Eisenstein series. In this paper, continuing his work, we consider generalized non-holomorphic Eisenstein series and give an analytic continuation to the s-plane.
참고문헌 (11)
- B. C. Berndt, "Two new proofs of Lerch's functional equation", Proc. Amer. Math. Soc, 32, pp.403~408 (1972)
- B. C. Berndt, "Generalized Eisenstein series and modified Dedekind sums", J. Reine. Angew. Math, 272, pp.182~193 (1975)
- B. C. Berndt, "Modular transformations and generalizations of several formulae of Ramanujan", The Rocky mountain J. Math, 7(1), pp.147~189 (1977)
- B. C. Berndt, "Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan", J. Reine. Angew. Math, 304, pp.332~365 (1978)
- M. Katsurada, "Differential actions on the asymptotic expansions of non-holomorphic Eienstein series, to appear", ~
- N. N. Lebedev, "Special functions and their applications" (1972), Dover Publications, Inc.
- S. Lim, "Generalized Eisenstein series and several modular transformation formu- lae", Ramanujan J, 19, pp.121~136 (2009)
- S. Lim, "Modular transformation formulae for non-holomorphic Eisenstein series, to appear", ~
- P. Pasles, "A generalization of the Lipschitz summation formula and applications", Proc. Ams. Math. Soc, 129(11), pp.3177~3184 (2001)
- L. J. Slater, "Con uent hypergeometric functions" (1960), Cambridge University Press
- E. C. Titchmarsh, "Theory of functions" (1952), Oxford University Press
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