Areal velocity equal to the magnitude of the cross product of vectors "AB" and "AC". This area can also be viewed as a vector with this magnitude, pointing in a direction perpendicular to the parallelogram; this vector is the cross product itself: Hence The areal velocity is this vector area divided by Δ"t" in the limit that Δ"t" becomes vanishingly small: But, formula_4 is the velocity vector formula_5 of the moving particle, so that On the other hand, the angular momentum of the particle is and hence the angular momentum equals 2"m" times the areal velocity. Conservation of areal velocity is a
Smith–Minkowski–Siegel mass formula all the "p"-masses have their standard value, then the total mass is the standard mass where The values of the Riemann zeta function for an even integers "s" are given in terms of Bernoulli numbers by So the mass of "ƒ" is given as a finite product of rational numbers as If the form "f" has a p-adic Jordan decomposition where "q" runs through powers of "p" and "f" has determinant prime to "p" and dimension "n"("q"), then the "p"-mass is given by Here "n"(II) is the sum of the dimensions of all Jordan components of type 2 and "p"