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 ...

To solve the problem, Tao measured the “entropy” of mathematical objects called multiplicative functions or sequences, which lie at the heart of not just the Erdős discrepancy problem, but ...

In this note, it is proved the existence of an infinitely generated multiplicative group consisting of entire functions that are, except for the constant function 1, hypercyclic with respect to the ...

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 ...

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 ...