On finding many solutions to S-unit equations by solving linear equations on average

Details On finding many solutions to S-unit equations by solving linear equations on average On finding many solutions to S-unit equations by solving linear equations on average

2011-08-18

arxiv.org/abs/1108.3819v1

Mathematics

Number Theory

32 pages

Scientific paper

We give improved lower bounds for the number of solutions of some $S$-unit equations over the integers, by counting the solutions of some associated linear equations as the coefficients in those equations vary over sparse sets. This method is quite conceptually straightforward, although its successful implementation involves, amongst other things, a slightly subtle use of a large sieve inequality. We also present two other results about solving linear equations on average over their coefficients.

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