Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

CHARACTER ANALOGUES OF INFINITE SERIES FROM A CERTAIN MODULAR TRANSFORMATION FORMULA

  • Lim, Sung-Geun (DEPARTMENT OF MATHEMATICS POHANG UNIVERSITY OF SCIENCE AND TECHNOLOGY)
  • Received : 2009.05.29
  • Accepted : 2010.02.12
  • Published : 2011.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we find character analogues of infinite series identities which come from a certain modular transformation formula given by B. C. Berndt.

Keywords

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, Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan, J. Reine Angew. Math. 303/304 (1978), 332-365.
  3. B. C. Berndt, A. Dixit, and J. Sohn, Character analogues of formulas of Ramanujan, Koshliakov and Guinand, to appear in Adv. in Appl. Math.
  4. H. H. Chan, On the equivalence of Ramanujan's partition identities and a connection with the Rogers-Ramanujan continued fraction, J. Math. Anal. Appl. 198 (1996), no. 1, 111-120. https://doi.org/10.1006/jmaa.1996.0071
  5. A. P. Guinand, Some rapidly convergent series for the Riemann ${\varepsilon}-function$, Quart. J. Math. Oxford Ser. (2) 6 (1955), 156-160. https://doi.org/10.1093/qmath/6.1.156
  6. S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.