Andrew Granville's Home Page

1998 Publications

On the exponential sum over \( k\)-free numbers (with Joerg Brudern, Alberto Perelli, Bob Vaughan and Trevor Wooley )
Philosophical Transactions of the Royal Society, 356 (1998), 739-761.

We give upper and lower bounds for exponential sums over \( k\)-power free numbers


A binary additive problem of Erdös and the order of \(2 \pmod {p^2}\) (with K. Soundararajan )
Ramanujan Journal, 2 (1998), 283-298.

We show that the problem of representing every odd integer as the sum of a squarefree number and a power of 2 is strongly related to the problem of showing that \( p^2\) divides \( 2^{p-1}-1\) for few primes \( p\).


ABC allows us to can count squarefrees,
International Mathematical Research Notices, 19 (1998), 991-1009.

We show that the \( abc\)-conjecture allows one to give the appropriate estimate for the number of squarefree values of any given polynomial

A journalistic article on the breakthrough of Friedlander and Iwaniec on primes of the form \( a^2+b^4\)