Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON THE GENERALIZED TWO VARIABLE EISENSTEIN SERIES

  • Lim, Sung-Geun (Department of Mathematics Education, Mokwon University)
  • Received : 2014.10.20
  • Accepted : 2014.11.16
  • Published : 2014.12.25
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Abstract

In this paper, we consider generalized two variable Eisenstein series. We give analytic continuation and prove modular transformation formulae for them.

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References

  1. B. C. Berndt, Two new proofs of Lerch's functional equation, Proc. Amer. Math. Soc. 32 (1972), 403-408.
  2. B. C. Berndt, Modular transformations and generalizations of several formulae of Ramanujan, The Rocky mountain J. Math. 7(1) (1977), 147-189. https://doi.org/10.1216/RMJ-1977-7-1-147
  3. N. N. Lebedev, Special functions and their applications, Dover Publications, Inc., New York, 1972.
  4. S. Lim, Analytic continuation of generalized non-holomorphic Eisenstein series, Korean J. Math. 21(3) (2013), 285-292. https://doi.org/10.11568/kjm.2013.21.3.285
  5. S. Lim, Modular transformation formulae for generalized non-holomorphic Eisen-stein series, Honam Mathematical J. 35(3) (2013), 507-513. https://doi.org/10.5831/HMJ.2013.35.3.507
  6. P. Pasles and W. Pribitkin, A generalization of the Lipschitz summation formula and applications, Proc. Ams. Math. Soc. 129(11) (2001), 3177-3184. https://doi.org/10.1090/S0002-9939-01-06038-5

Cited by

  1. Transformation formulae and asymptotic expansions for double holomorphic Eisenstein series of two complex variables vol.44, pp.2, 2017, https://doi.org/10.1007/s11139-017-9922-5