Modular Equations of Higher and Composite Degrees

Bruce C. Berndt
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Bruce C. Berndt: University of Illinois at Urbana-Champaign, Department of Mathematics

Chapter Chapter 20 in Ramanujan’s Notebooks, 1991, pp 325-453 from Springer

Abstract: Abstract In this chapter, we continue to examine Ramanujan’s discoveries about modular equations. In the previous chapter, modular equations of degrees 3, 5, and 7 were derived. Modular equations of degrees 11, 13, 17, 19, 23, 31, 47, and 71 are established in this chapter. Also, modular equations of composite degree, or “mixed” modular equations, are studied. Most of the equations of the latter type involve four distinct moduli, and so we begin by defining such a modular equation.

Keywords: Modular Form; Rational Part; Elementary Algebra; Modular Equation; Multiplier System (search for similar items in EconPapers)
Date: 1991
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DOI: 10.1007/978-1-4612-0965-2_6

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