An explicit formula is given for the representation number of each of the 75 reduced, positive-definite, integral, primitive, quaternary quadratic forms ax2 + bxy + cy2 + dz2 + ezt + ft2, which belong to a genus with discriminant ≤ 1732 containing one and only one form class.

Additional Metadata
Keywords Dirichlet L-series, double Gauss sums, genus of quaternary quadratic forms, local density, modular forms, Representation number, Siegel's mass formula, sum of two binary quadratic forms, theta functions
Persistent URL dx.doi.org/10.1142/S1793042116500950
Journal International Journal of Number Theory
Citation
Alaca, A, Alaca, S, & Williams, K.S. (2016). Representation numbers of certain quaternary quadratic forms in a genus consisting of a single class. International Journal of Number Theory, 12(6), 1529–1573. doi:10.1142/S1793042116500950