Experts crack Ramanujan’s algebra riddle

Kounteya Sinha TNN

London: Mathematicians have found a framework for the celebrated Rogers-Ramanujan identities and their arithmetic properties, solving another long-standing mystery stemming from the work of Indian math genius Srinivasa Ramanujan. The solution was found by mathematicians at Emory University and the University of Queensland.
    “Algebraic numbers are among the first numbers you encounter in mathematics and yet it’s difficult to find functions that return them as values in a uniform and systematic way,” said Ken Ono, a number theorist at Emory. “A fundamental problem in mathematics is to find functions whose values are always algebraic numbers,” he said. Ramanujan could produce such numbers, and he made it look easy. The Rogers-Ramanujan identities are considered among his greatest legacies. The identities were originally discovered by L J Rogers in 1894.
    In 1913, Ramanujan sent a letter to British mathematician G H Hardy that included the two identities that Rogers discovered and a third formula that showed these identities are essentially modular functions and their quotient has the special property that its singular values are algebraic integral units. That result came to be known as the Rogers-Ramanujan continued fraction. Ramanujan died in 1920 before he could explain how he conjured up the formulas. For nearly a century, experts have tried to solve the mystery. 

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