Abstract
We improve an estimate of A. Granville (1987) on the number of vanishing Fermat quotients qp(ℓ) modulo a prime p when ℓ runs through primes ℓ≤N. We use this bound to obtain an unconditional improvement of the conditional (under the Generalised Riemann Hypothesis) estimate of Y. Ihara (2006) on a certain sum, related to vanishing Fermat quotients. In turn this sum appears in the study of the index of certain subfields of cyclotomic fields Q(exp(2πi=p2)).
Original language | English |
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Pages (from-to) | 99-108 |
Number of pages | 10 |
Journal | Kodai Mathematical Journal |
Volume | 36 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2013 |