The relative growth rate for partial quotients.
The relative size of consecutive odd denominators in Farey series.
The representation of almost all numbers as sums of unlike powers
We prove in this article that almost all large integers have a representation as the sum of a cube, a biquadrate, ..., and a tenth power.
The representation of one quadratic form by another in valuated fields
The representation of primes by cubic polynomials
The representation of primes by quadratic and cubic polynomials
The representation of real numbers by infinite series of rationals
The representation of squares to the base 3
The residual spectrum of
The resolution of the diophantine equation x(x+d)...(x+(k-1)d) = by² for fixed d
The restricted Toda chain, exponential Riordan arrays, and Hankel transforms.
The restriction to of a supercuspidal representation of
The Rhin-Viola method for log 2
The “Riemann hypothesis” for the Hawkins random Sieve
The Riemann Zeta function and coin tossing.
The ring of arithmetical functions with unitary convolution: Divisorial and topological properties
We study , the ring of arithmetical functions with unitary convolution, giving an isomorphism between and a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett [NumThe] between the ring of arithmetical functions with Dirichlet convolution and the power series ring on countably many variables. We topologize it with respect to a natural norm, and show that all ideals are quasi-finite. Some elementary results on factorization into atoms...
The ring of integers of an abelian number field.
The role of functional equations in stochastic model building.
The role of semigroups in the elementary theory of numbers
The role of the Lagrange constant in some nonlinear waves equations.