On vanishing Fermat quotients and a bound of the Ihara sum

Kodai Mathematical Journal

Igor E. Shparlinski¹ 

[1] Department of Computing Macquarie University

关键词: Fermat quotient;    Ihara sum;    cyclotomic field;   

DOI  :  10.2996/kmj/1364562722

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(13)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)).

【 授权许可】

Unknown