On a Modular Equation of Degree 27


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


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.


Theta Functions, Modular Equations.

Subject Discipline

Mathematical Sciences

Full Text:


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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