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ERC Research Period on Diophantine Geometry

Perfect powers with few binary digits (40')

speaker: Yann Bugeaud (Université de Strasbourg)

abstract: We prove that, for any fixed base x at least equal to 2 and any sufficiently large prime q, no perfect q-th powers can be written with 3 or 4 digits 1 in base x. We also establish that if q is an integer at least equal to 5, then every q-th power of an integer contains at least 5 digits 1 in its binary expansion.These are particular instances of rather more general results, whose proofs follow from a combination of refined lower bounds for linear forms in Archimedean and non-Archimedean logarithms. This is a joint work with M. Bennett and M. Mignotte.

timetable:
Fri 5 Oct, 10:30 - 11:10, Sala Conferenze Centro De Giorgi
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