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