Therefore taking the product of the Dedekind zeta-functions of the quadratic fields, multiplying them together, and dividing by the square of the Riemann zeta-function, is a recipe for the Dedekind zeta-function of the biquadratic field.
32.
For example, if the smoothing process is to always apply a biquadratic ( two-pole, two-zero ) filter forward then backwards on each row of data ( and on each column in the 2D case ), the poles and zeros can each do a part of the smoothing.
33.
The theorems on biquadratic residues gleam with the greatest simplicity and genuine beauty only when the field of arithmetic is extended to "'imaginary "'numbers, so that without restriction, the numbers of the form " a " + " bi " constitute the object of study . . . we call such numbers "'integral complex numbers "'. [ bold in the original]
34.
The theorems on biquadratic residues gleam with the greatest simplilcity and genuine beauty only when the field of arithmetic is extended to "'imaginary "'numbers, so that without restriction, the numbers of the form " a " + " bi " constitute the object of study . . . we call such numbers "'integral complex numbers "'. [ bold in the original]
