An asymptotic expansion for the counting function of semiprimes

10 May 2021
16:00
Dragos Crisan
Abstract

A semiprime is a natural number which can be written as the product of two primes. Using elementary methods, we'll explore an asymptotic expansion for the counting function of semiprimes $\pi_2(x)$, which generalises previous findings of Landau, Delange and Tenenbaum.  We'll also obtain an efficient way of computing the constants involved. In the end, we'll look towards possible generalisations for products of $k$ primes.

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  • Junior Number Theory Seminar