Exact Exponent of Remainder Term of Gelfond's Digit Theorem in Binary Case

TL;DR

This paper provides a precise formula for the exponent in the remainder term of Gelfond's digit theorem specifically for binary numbers, enhancing understanding of digit distribution in binary expansions.

Contribution

The paper introduces a simple, exact formula for the exponent in the remainder term of Gelfond's digit theorem in the binary case, improving upon previous bounds.

Findings

Derived a simple formula for the exact exponent

Refined the understanding of digit distribution in binary

Enhanced the precision of Gelfond's digit theorem

Abstract

We give a simple formula for the exact exponent in the remainder term of the main Gelfond's digit theorem in the binary case.