Siegel's formula for genus 2

Let S be a semi-integral, symmetric, positive-definite m x m matrix; mn1. By the Siegel fundamental formula we mean the identity between the Siegel theta series of genus n, associated with the genus of the matrix S, and the correspond ing Eisenstein-Siegel series (C. L. Siegel, Lectures on the Analytical Theory of Quadratic Forms, 3rd rev. edition, Peppmüller, Göttingen, 1963). The validity of the mentioned formula for m/2n+1 is an open problem in the general case. In this paper we prove Siegel's formula for n=2, m=6.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 76, pp. 210–215, 1978.