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A317965 Representation numbers (or theta series) for either one of Schiemann's pair of four-dimensional positive definite quadratic forms with the same representation numbers. 1

%I

%S 1,0,2,0,4,6,10,6,12,6,6,8,10,8,10,22

%N Representation numbers (or theta series) for either one of Schiemann's pair of four-dimensional positive definite quadratic forms with the same representation numbers.

%C a(n) is the number of ways either form represents 2n.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, Third edition, p. xxix.

%D Earnest, A. G., and G. Nipp. "On the theta series of positive quaternary quadratic forms." CR Math. Rep. Acad. Sci. Canada 13 (1991): 33-38. See p. 36.

%D Schiemann, Alexander. "Ein Beispiel positiv definiter quadratischer Formen der Dimension 4 mit gleichen Darstellungszahlen." Archiv der Mathematik, 54.4 (1990): 372-375.

%H J. H. Conway and N. J. A. Sloane, <a href="http://NeilSloane.com/doc/nipp.pdf">Four-Dimensional Lattices With the Same Theta Series</a>, Duke Math. J., 66 (International Mathematics Research Notices Number 4) (1992), pp. 93-96. (Pages are in reverse order)

%K nonn,more

%O 0,3

%A _N. J. A. Sloane_, Aug 26 2018

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Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)