Abstract
We derive Jacobi's quartic identity and the Borweins' cubic identity related to Ramanujan's quadratic modular equation on theta series by lattice enumerative methods. Both identities are instrumental in recent work of the Borweins on the Arithmetic Geometric Mean. Of great use are the constructions of the root lattices D 4 and E 6 by binary and ternary codes respectively. A third identity, equally due to the Borweins is also derived in relation to the root lattice E 8.
On leave of absence from CNRS, I3S, 250 rue A. Einstein, 06560 Valbonne, France
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© 1995 Springer-Verlag Berlin Heidelberg
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Sole, P. (1995). D4, E6, E8 and the AGM. In: Cohen, G., Giusti, M., Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1995. Lecture Notes in Computer Science, vol 948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60114-7_35
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DOI: https://doi.org/10.1007/3-540-60114-7_35
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