Odd prime values of the Ramanujan tau function |
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Authors: | Nik Lygeros Olivier Rozier |
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Affiliation: | 1. LGPC (UMR 5285), Université de Lyon, 69616, Villeurbanne, France 2. Service de calcul parallèle S-CAPAD, IPGP (UMR 7154), 75238, Paris, France
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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):=τ(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. |
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