Effective mass (solid-state physics) from both sides gives where is the th element of , is the th element of , and are the th and th elements of , respectively, and is the total energy of the particle according to the Planck–Einstein relation. The index is contracted by the use of Einstein notation (there is an implicit summation over ). Since Newton's second law uses the inertial mass (not the gravitational mass), we can identify the inverse of this mass in the equation above as the tensor This tensor expresses the change in group velocity due to a change in crystal momentum. Its
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"