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# New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function.

@article{Milne1996NewIF, title={New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function.}, author={Stephen C. Milne}, journal={Proceedings of the National Academy of Sciences of the United States of America}, year={1996}, volume={93 26}, pages={15004-8} }

- Published 1996 in Proceedings of the National Academy of Sciences…

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi's (1829) 4 and 8 squares identities to 4n(2) or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan's tau function tau(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace… CONTINUE READING