Primitive root bias for twin primes II: Schinzel-type theorems for totient quotients and the sum-of-divisors function
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F20%3AA210248O" target="_blank" >RIV/61988987:17310/20:A210248O - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022314X19302835" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022314X19302835</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jnt.2019.08.003" target="_blank" >10.1016/j.jnt.2019.08.003</a>
Alternative languages
Result language
angličtina
Original language name
Primitive root bias for twin primes II: Schinzel-type theorems for totient quotients and the sum-of-divisors function
Original language description
Garcia, Kahoro, and Luca showed that the Bateman-Horn conjecture implies phi(p - 1) >= phi(p+ 1) for a majority of twin-primes pairs p, p + 2 and that the reverse inequality holds for a small positive proportion of the twin primes. That is, p tends to have more primitive roots than does p + 2. We prove that Dickson's conjecture, which is much weaker than Bateman-Horn, implies that the quotients phi(p+1)/phi(p-1), as p, p + 2 range over the twin primes, are dense in the positive reals. We also establish several Schinzel-type theorems, some of them unconditional about the behavior of phi(p+1)/phi(p) and sigma(p+1)/sigma(p), in which sigma denotes the sum-of-divisors function.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-02804S" target="_blank" >GA17-02804S: Properties of number sequences and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
J NUMBER THEORY
ISSN
0022-314X
e-ISSN
—
Volume of the periodical
208
Issue of the periodical within the volume
March
Country of publishing house
US - UNITED STATES
Number of pages
18
Pages from-to
400-417
UT code for WoS article
000499759700019
EID of the result in the Scopus database
2-s2.0-85072822678