Limiting distributions of the classical error terms of prime number theory

2013/06/07 by Amir Akbary, Akbary, Amir, Nathan Ng +3 · 2 citations
Mathematics · Social Sciences · #11M06 #11M26 #Analytic Number Theory Research #FOS: Mathematics #Historical Geopolitical and Social Dynamics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1306.1657

openalex publication_date 2013/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we prove a general theorem which establishes the existence of limiting distributions for a wide class of error terms from prime number theory. As a corollary to our main theorem, we deduce previous results of Wintner (1935), Rubinstein and Sarnak (1994), and of Ng (2004). In addition, we establish limiting distribution results for the error term in the prime number theorem for an automorphic L-function, weighted sums of the Möbius function, weighted sums of the Liouville function, the sum of the Möbius function in an arithmetic progression, and the error term in Chebotarev's density theorem.

Cited by

• Joint distributions of error terms for primes in arithmetic progressions modulo 11
• A bias in Mertens' product formula

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