JournalspmVol. 64 / No. 2DOI 10.4171/pm/1779

Euler constants for the ring of <em>S</em>-integers of a function field

  • Mireille Car

    Université Aix-Marseille III, France
Euler constants for the ring of <em>S</em>-integers of a function field cover

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Abstract

The Euler constant may be defined as the limit for tending to , of the difference . Alternatively, it may be defined as the limit at 1 of the difference , being a complex number in the half-plane . Mertens theorem states that for real number tending to +, , the product being over prime numbers . We prove analog results for the ring of -integers of a function field. However, in the function field case, the three approaches lead to different constants.