Periods of rational maps modulo primes

• Let K be a number field, let be a rational map of degree at least 2, and let . We show that if alpha is not in the forward orbit of beta, then there is a positive proportion of primes of K such that is not in the forward orbit of . Moreover, we show that a similar result holds for several maps and several points. We also present heuristic and numerical evidence that a higher dimensional analog of this result is unlikely to be true if we replace alpha by a hypersurface, such as the ramification locus of a morphism .

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Polynomials

Orbits

Publikations- och innehållstyp

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