Asymmetries in the Shanks-Renyi Prime Number Race
| dc.creator | Martin, Greg | |
| dc.date | 2000-10-09 | |
| dc.date | 2000-11-17 | |
| dc.date.accessioned | 2026-07-07T04:37:55Z | |
| dc.date.available | 2026-07-07T04:37:55Z | |
| dc.description | It has been well-observed that an inequality of the type $π(x;q,a) > π(x;q,b)$ is more likely to hold if $a$ is a non-square modulo $q$ and $b$ is a square modulo $q$ (the so-called ``Chebyshev Bias''). For instance, each of $π(x;8,3)$, $π(x;8,5)$, and $π(x;8,7)$ tends to be somewhat larger than $π(x;8,1)$. However, it has come to light that the tendencies of these three $π(x;8,a)$ to dominate $π(x;8,1)$ have different strengths. A related phenomenon is that the six possible inequalities of the form $π(x;8,a_1) > π(x;8,a_2) > π(x;8,a_3)$ with $\{a_1,a_2,a_3\}=\{3,5,7\}$ are not all equally likely---some orderings are preferred over others. In this paper we discuss these phenomena, focusing on the moduli $q=8$ and $q=12$, and we explain why the observed asymmetries (as opposed to other possible asymmetries) occur. | |
| dc.description | 11 pages; submitted to the conference proceedings of the Millennial Conference on Number Theory (University of Illinois at Urbana-Champaign, 2000). Minor revisions only | |
| dc.identifier | https://arxiv.org/abs/math/0010086 | |
| dc.identifier | http://arxiv.org/abs/math/0010086 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60085 | |
| dc.subject | Number Theory | |
| dc.subject | 11N15 (11N69) | |
| dc.title | Asymmetries in the Shanks-Renyi Prime Number Race | |
| dc.type | text |