Oscillations in Mertens Theorems and Other Finite Sums and Products

Mathematics – Number Theory

Scientific paper

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Improved Version, 13 Pages

Scientific paper

This note simplifies the proof of a recent result on the oscillation of the
prime product in Martens Theorem, and provides a quantitative expression for
the error term. In addition, the corresponding oscillation results for the
finite sums of the reciprocal of the primes up to a fixed number and other
finite sums and products are also given.

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