A Remark on Sieving in Biased Coin Convolutions

TL;DR

This paper investigates the distribution properties of densities generated by biased coin convolutions and applies sieving theory to estimate their behavior on pseudo-primes, revealing new insights into their structure.

Contribution

It establishes a nontrivial level of distribution for densities from biased coin convolutions and derives lower bounds for their weights on pseudo-primes using sieving theory.

Findings

Established a nontrivial level of distribution for biased coin convolution densities.

Derived lower bounds for the weight of these densities on pseudo-primes.

Connected convolution densities with sieving theory to analyze their distribution.

Abstract

In this work, we establish a nontrivial level of distribution for densities on $\{1,\ldots, N\}$ obtained by a biased coin convolution. As a consequence of sieving theory, one then derives the expected lower bound for the weight of such densities on sets of pseudo-primes.