Tuesday, April 12 2022, 10:00 – 11:00, M113

One of the central topics in the theory of Beurling generalized primes is the relationship between the counting function of the generalized primes and the counting function of the generalized integers. In this talk we discuss the case when one of the two has an asymptotic formula with a so-called Malliavin remainder x exp(-c(\log x)^{alpha}). (Note that power-type remainders x^{theta} are a special case of this.) We indicate what kind of remainder this asymptotic formula implies for the other counting function. We share some recent work on this problem, and discuss a conjecture about the optimal remainders.