We also obtain some additional results on smooth numbers in almost all intervals, and sign changes of multiplicative functions in all intervals of square-root length. Annals of Mathematics, a ...

Character sums – often constructed using Dirichlet characters or other multiplicative functions – play a crucial role in probing the distribution of primes, quadratic residues, and non ...

Nobuhiro Asai, Izumi Kubo, Hui-Hsiung Kuo, MULTIPLICATIVE RENORMALIZATION AND GENERATING FUNCTIONS I, Taiwanese Journal of Mathematics, Vol. 7, No. 1 (March 2003), pp. 89-101 ...

Tao says he all but forgot about the problem until this year, when he started working with a pair of mathematicians who had achieved a major insight into what are called multiplicative functions.

Multiplicative functions are very important in number theory and have been the subject of intense study for centuries, so this was an important step.

“We had figured out an interesting reduction of the Erdős discrepancy problem to a seemingly simpler problem involving a special type of sequence called a completely multiplicative function ...