A multiplicative function is defined on the positive integers and its rule is completely determined by its values on prime powers, according with the prime factorization. A random multiplicative function is obtained by keeping the multiplicative rule and by assigning to each prime number a random variable.
In this talk I am going to show some classical and new results about the partial sums of a multiplicative function, and how the (unknown) mean behavior of these partial sums is closely related with the Riemann Hypothesis.
This is based on joint work with Vladas Sidoravicius.
Biography
Marco Aymone is currently an assistant Professor at Federal University from Minas Gerais - UFMG, Brazil. He obtained his Ph.D. in mathematics at IMPA, Rio de Janeiro, Brazil, under the supervision of Prof. Vladas Sidoravicius. His research interests include Number Theory, Probability Theory and Statistical Physics.