Here the asymptotic prime decomposition of round numbers is found. These are numbers which have a number of divisors greater than any number less than themselves.

Certain trigonometric sums.

Here it is proved that the porportion of q-numbers in intervals [1, n] for particular values of n is greater than for any other m>n.

Computation of the order n momenta for the function ω(i), equal to the number of prime divisors of i.

Thread leading from Thue's theorem to Roth's.