Leading Digits of Some P-Adic Numbers

Author

Jinha Park, Boise State UniversityFollow

Publication Date

5-2025

Date of Final Oral Examination (Defense)

3-5-2025

Type of Culminating Activity

Thesis

Degree Title

Master of Science in Mathematics

Department

Mathematics

Supervisory Committee Chair

Zachariah Teitler, Ph.D.

Supervisory Committee Member

Jens Harlandar, Ph.D.

Supervisory Committee Member

Marion Scheepers, Ph.D.

Abstract

I investigated the leading digits of some sequences in the p-adic numbers Q_p, hoping to find some sequences following Benford's law, or following something completely different. We found that the sequence of partial sums Sum^N_{n=1}\frac{1}{n^s}, where s\in\N is fixed, shows uneven distribution of leading digits, except for s\equiv 0 (mod{p,/em>-1}), where the distribution of leading digits is eventually even. We were able to characterize the distribution of this partial sum for almost all s.