On a Modular Equation of Degree 27


Affiliations

  • University of Mysore, Department of Studies in Mathematics, Mysore, 570006, India

Abstract

On page 309 of his second notebook, Ramanujan has recorded a modular equation of composite degree 1, 3, 9, 27. B. C. Berndt has dis-proved the same and did not mention the correct one. The purpose of this paper is to establish the same.

Keywords

Theta Functions, Modular Equations.

Subject Discipline

Mathematical Sciences

Full Text:

References

B. C. Berndt, Ramanujan’s Notebooks, Part III, Springer-Verlag, New York, 1991.

B. C. Berndt, Ramanujan’s Notebooks, Part V, Springer-Verlag, New York, 1998.

S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.

K. R. Vasuki, On certain Ramanujan-Weber type Modular Equations, J. Indian Math. Soc., 75 (1-4)(2008), 173–192.

H. Weber, Zur Theorie der elliptischen Functionen, Acta Math., 11 (1887-88), 333–390.


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