Odd prime values of the Ramanujan tau function - Université Claude Bernard Lyon 1 Access content directly
Journal Articles Ramanujan Journal Year : 2013

Odd prime values of the Ramanujan tau function

Abstract

We study the odd prime values of the Ramanujan tau function, which form a thin set of large primes. To this end, we define LR(p,n):=tau(p (n-1)) and we show that the odd prime values are of the form LR(p,q) where p,q are odd primes. Then we exhibit arithmetical properties and congruences of the LR numbers using more general results on Lucas sequences. Finally, we propose estimations and discuss numerical results on pairs (p,q) for which LR(p,q) is prime.

Dates and versions

hal-01930804 , version 1 (22-11-2018)

Identifiers

Cite

Nik Lygeros, Olivier Rozier. Odd prime values of the Ramanujan tau function. Ramanujan Journal, 2013, 32 (2), pp.269 - 280. ⟨10.1007/s11139-012-9420-8⟩. ⟨hal-01930804⟩
125 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More