Abstract
The goal of this article is to associate a p-adic analytic function to the Euler constants γp(a, F), study the properties of these functions in the neighborhood of s = 1 and introduce a p-adic analogue of the infinite sum \(\sum\limits_{n \geqslant 1} f (n)/n\)# for an algebraic valued, periodic function f. After this, we prove the theorem of Baker, Birch and Wirsing in this setup and discuss irrationality results associated to p-adic Euler constants generalising the earlier known results in this direction. Finally, we define and prove certain properties of p-adic Euler-Briggs constants analogous to the ones proved by Gun, Saha and Sinha.
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Acknowledgements
The author thanks Sanoli Gun for suggesting the analogue of Generalised Euler Briggs constant, on which the last section is based. The author also thanks the referee for the suggestions which improved the presentation of the paper. The author thanks the INFOSYS for generous funding.
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Bharadwaj, A. On p-ADIC Euler Constants. Czech Math J 71, 283–308 (2021). https://doi.org/10.21136/CMJ.2020.0336-19
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DOI: https://doi.org/10.21136/CMJ.2020.0336-19