[D66] The Riemann Zeta Function Across Number Bases: A Study of Notational Elegance

[René Oudeweg]

[new paper]

The Riemann Zeta Function Across Number Bases:
A Study of Notational Elegance
René Oudeweg / Claude Opus
January 2, 2026

Abstract
We explore the representation of the Riemann zeta function and its 
special values in various number bases, with particular emphasis on base 
4 and base 12. We demonstrate that while the mathematical properties of 
the zeta function remain invariant under change of base, certain bases 
provide notational elegance for specific values. Notably, base 12 offers 
a remarkably simple representation of the Ramanujan summation

ζ(−1) = − 1/12

and we explore connections to the Riemann Hypothesis through the
critical line Re(s) = 1/2
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