Two results on Beurling generalized numbers
Harold George Diamond · Publicationes Mathematicae Debrecen · 2011
A sequence of Beurling generalized primes (g-primes) is an unbounded sequence of real numbers P = {pi} satisfying 1 ≤ p1 ≤ p2 ≤ . . . .The multiplicative semigroup generated by P along with 1 is designated as the corresponding collection of g-integers N .Here we give a brief survey of Beurling numbers and then describe two achievements of recent years: the L 2 prime number theorem of Kahane and the oscillation result of Diamond, Montgomery, and Vorhauer.