Linear relations of theta series of genera of quadratic forms (Q854016)

This paper generalizes previous work of the authors [Acta Arith. 116, No. 4, 387--398 (2005; Zbl 1143.11312)] from ternary forms to \(n\)-ary forms for odd \(n\geq 5\). Here the authors study linear relations among theta series of genera of positive definite \(n\)-ary quadratic forms with given level \(D\), \(2D\), \(4D\) and \(8D\) for square free \(D\). They obtain a basis for the space generated by genus theta series. This forms a basis of Eisenstein space.