Primitive root bias for twin primes. II: Schinzel-type theorems for totient quotients and the sum-of-divisors function

DOI10.1016/j.jnt.2019.08.003zbMath1450.11002arXiv1906.05927OpenAlexW2976384751MaRDI QIDQ2009171

Florian Luca, Kye Shi, Gabe Udell, Stephan Ramon Garcia

Publication date: 27 November 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.05927

zbMATH Keywords

primitive rootprimetwin primetwin prime conjectureChen's theoremtotient functionBateman-Horn conjectureDickson's conjectureprime bias

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Congruences; primitive roots; residue systems (11A07) Distribution of primes (11N05) Rate of growth of arithmetic functions (11N56) Primes (11A41)

Related Items (3)

Totient quotient and small gaps between primes ⋮ Lateral Movement in Undergraduate Research: Case Studies in Number Theory ⋮ Multidimensional Schinzel-type theorems for multiplicative functions near prime tuples

Cites Work

• Variants of the Selberg sieve, and bounded intervals containing many primes
• New equidistribution estimates of Zhang type
• Primitive root biases for prime pairs. I: Existence and non-totality of biases
• Bounded gaps between primes
• On the Difference in Values of the Euler Totient Function Near Prime Arguments
• A note on some properties of the functions φ (n), σ(n) and θ(n)
• Some remark on Euler's φ function
• A Heuristic Asymptotic Formula Concerning the Distribution of Prime Numbers
• Handbook of Number Theory I
• Primitive Root Bias for Twin Primes
• Small gaps between primes
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