A new method for binary additive problems
by
Jörg Brüdern
University of Stuttgart

This talk concerns binary additive problems for sequences of positive density which in addition are also reasonably well distributed in arithmetic progressions. We investigate to what extent the circle method is able to handle a binary additive problem for such sequences. It turns out that this is indeed possible for a large class of sequences. To mention just one special case, we are able to prove the following: Let A, B denote multiplicative sequences with positive density. Let r(n) denote the number of representations n=a+b with a in A, b in B. Then, one has an asymptotic formula r(n) ~ n S(n) where S(n) is a formal singular series (in practise, a product of local densities).

Date received: March 15, 2000