On Grosswald's conjecture on primitive roots

• Autorzy: Stephen D. Cohen , Tomás Oliveira e Silva , Tim Trudgian
• Języki publikacji: EN

Abstrakty

EN

Grosswald's conjecture is that g(p), the least primitive root modulo p, satisfies g(p) ≤ √p - 2 for all p > 409. We make progress towards this conjecture by proving that g(p) ≤ √p -2 for all $409 < p < 2.5 × 10^{15}$ and for all $p > 3.38 × 10^{71}$.

Kategorie tematyczne

• 11L40: Estimates on character sums
• 11A07: Congruences; primitive roots; residue systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 172
• Numer: 3
• Strony: 263-270

Daty

wydano

2016

Twórcy

autor

Stephen D. Cohen

• School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, Scotland

autor

Tomás Oliveira e Silva

• Departamento de Electrónica,, Telecomunicações e Informática, Universidade de Aveiro, 3810-193 Aveiro, Portugal

autor

Tim Trudgian

• Mathematical Sciences Institute, The Australian National University, Canberra, ACT 2601, Australia

Identyfikatory

DOI

10.4064/aa8109-12-2015