Automata and transcendence of the Tate period in finite characteristic

Allouche, Jean-Paul; Thakur, Dinesh

doi:10.1090/S0002-9939-99-04650-X

Automata and transcendence of the Tate period in finite characteristic
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by Jean-Paul Allouche and Dinesh S. Thakur PDF

Proc. Amer. Math. Soc. 127 (1999), 1309-1312 Request permission

Abstract:

Using the techniques of automata theory, we give another proof of the function field analogue of the Mahler-Manin conjecture and prove transcendence results for the power series associated to higher divisor functions $\sigma _k(n)=\sum _{d|n}d^k$.

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