Heuristic formula for logarithm of the Frobenius morphism

Details Heuristic formula for logarithm of the Frobenius morphism Heuristic formula for logarithm of the Frobenius morphism

2010-11-08

arxiv.org/abs/1011.1865v1

Mathematics

Algebraic Geometry

2 pages

Scientific paper

We show that the logarithm $\log_q$ of the Frobenius morphism $x\to x^q$ is
given by the formula $x\to x\log x$ (the natural logarithm). In particular, it
does not depend on $q$. This is the explicit (although heuristical) formula for
the operator conjectured by Hilbert whose eigenvalues coincide with the zeroes
of the zeta function.

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