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Some Eisenstein series identities related to modular equation of the fourth order

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We find some Eisenstein series related to modulus 4 using a theta function identity of McCullough and Shen and residue theorem for elliptic functions.

Abstract

We find some Eisenstein series related to modulus 4 using a theta function identity of McCullough and Shen and residue theorem for elliptic functions.

참고문헌 (9)

  1. G. E. Andrews, "Ramanujan's Lost Notebook" (2005), Springer
  2. G. Gasper, "Basic Hypergeometric Series" (1990), Cambridge University Press
  3. Z.-G. Liu, "Some Eisenstein series identities", J. Number Theory, 85(2), pp.231~252 (2000)
  4. Z.-G. Liu, "Residue theorem and theta function identities", Ramanujan J, 5(2), pp.129~151 (2001)
  5. Z.-G. Liu, "Some theta functions identities associated with the modular equations of degree 5", Integers, 1(A3), pp.14~ (2001)
  6. Z.-G. Liu, "Some Eisenstein series identities related to modular equations of the seventh order", Paci c J. Math, 209(1), pp.103~130 (2003)
  7. S. McCullough, "On the Szeg~o kernel of an annulus", Proc. Amer. Math. Soc, 121(4), pp.1111~1121 (1994)
  8. S. Ramanujan, "Collected Papers" (1927), Cambridge University Press
  9. E. T. Whittaker, "A Course of Modern Analysis. An Introduction to the General Theory of In nite Processes and of Analytic Functions: with an account of the principal transcendental functions" (1962), Cambridge University Press

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