HUILAN LI, TRUEMAN MACHENRY, THE CONVOLUTION RING OF ARITHMETIC FUNCTIONS AND SYMMETRIC POLYNOMIALS, The Rocky Mountain Journal of Mathematics, Vol. 43, No. 4 (2013), pp. 1227-1259 ...

Recent investigations probe the arithmetic properties of these functions, exploring congruence relations and modular behaviour that reveal surprising regularities.

Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose ...