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On finding many solutions to S-unit equations by solving linear equations on average | | Adam J. Harper
; | | Date: |
18 Aug 2011 | | Abstract: | 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. | | Source: | arXiv, 1108.3819 | | Services: | Forum | Review | PDF | Favorites | |
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