On the Discrepancy of the Roots of x²+1 and x²+2 to Prime Moduli

2011/03/07 by Timothy Foo, Foo, Timothy
Mathematics · #Analytic Number Theory Research #Benford’s Law and Fraud Detection #math.NT #msc:11C08 #msc:11K06 #msc:11K38 #msc:11N32

paper · pdf · doi:10.48550/arxiv.1103.1253

This paper has been withdrawn

arxiv created 2012/10/03 · arxiv updated 2012/10/04

Abstract

In this paper, we make a conjecture (conjecture 1) related to the Bateman-Horn conjecture and proceed to study the roots of x²+1 and x²+2 to prime moduli, assuming the truth of the Bateman-Horn conjecture and conjecture 1 and using the Erdős-Turan-Koksma inequality.

Related

• Sectorial equidistribution of the roots of x² + 1 modulo primes
• A Note on the Bateman-Horn Conjecture
• The least primitive root modulo p²
• Topics In Primitive Roots
• Some experiments on Bateman-Horn