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}
}
  • Stephen C. Milne
  • 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