A numerical study of Siegel theta series of various degrees for the 48-dimensional even unimodular extremal lattices
It was proved by \textit{R. Salvati Manni} [J. Number Theory 83, No. 2, 282--296 (2000; Zbl 0957.11025)] that the difference of the Siegel theta series of degree \(4\) associated with the two even unimodular extremal lattices of \(48\) dimension is a constant multiple of the cube of the Schottky modular form. This implies that the Siegel theta series of degree \(\leq 3\) is unique. In this paper, the author gives a explicit computation of the Fourier coefficients of the Siegel theta series of degree \(2\) or \(3\) associated with the above mentioned \(48\)-dimensional lattices. Moreover, the author gives an almost explicit computation of the the Fourier coefficients of the Siegel theta series of degree \(4\) for the those lattices.
scientific article; zbMATH DE number 6710502