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An a b c d theorem over function fields and applications

Pietro Corvaja, Umberto Zannier (2011)

Bulletin de la Société Mathématique de France

We provide a lower bound for the number of distinct zeros of a sum 1 + u + v for two rational functions u , v , in term of the degree of u , v , which is sharp whenever u , v have few distinct zeros and poles compared to their degree. This sharpens the “ a b c d -theorem” of Brownawell-Masser and Voloch in some cases which are sufficient to obtain new finiteness results on diophantine equations over function fields. For instance, we show that the Fermat-type surface x a + y a + z c = 1 contains only finitely many rational or elliptic curves,...

An accurate approximation of zeta-generalized-Euler-constant functions

Vito Lampret (2010)

Open Mathematics

Zeta-generalized-Euler-constant functions, γ s : = k = 1 1 k s - k k + 1 d x x s and γ ˜ s : = k = 1 - 1 k + 1 1 k s - k k + 1 d x x s defined on the closed interval [0, ∞), where γ(1) is the Euler-Mascheroni constant and γ ˜ (1) = ln 4 π , are studied and estimated with high accuracy.

Currently displaying 1241 – 1260 of 1964