### 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

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#### 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 $$p$$.

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#### 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

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#### International team shows that primes can be found in surprising places, Resonance, 3 (1998), 71-72.

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

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