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arXiv:2403.03912 [math.NT]AbstractReferencesReviewsResources

Digamma function and general Fischer series in the theory of Kempner sums

Jean-François Burnol

Published 2024-03-06, updated 2024-03-07Version 2

The infinite sum of reciprocals of the integers which are missing specified digits (from a given base) is computed with the help of the digamma function as a series involving the zeta values at integers and certain quantities which are rational in the base. This generalizes the work of Fischer (1993) who had handled the original "no $9$ in base $10$" case.

Comments: 9 pages. v2 extended the comments after the main theorem and slightly changed the introduction
Categories: math.NT
Subjects: 11Y60, 11M06, 11A63, 44A60, 30C10
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