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A table of absolute norms of Heilbronn sums
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For each odd prime q an integer NHq (NH3 = −1, NH5 = −1, NH7 = 97, NH11 = −243, …) is defined as the norm from L to of the Heilbronn sum Hq = TrI(ζ)(ζ), where ζ is a primitive q2th root of unity and L ⊃- (ζ) the subfield of degree q. Various properties are proved relating the congruence properties of Hq and NHq modulo p (p ≠ q prime) to the Fermat quotient ; in particular, it is shown that NHq is even iff 2q − 1 ≡ 1 (mod q2).
Algebraic analysis and number theory (Kyoto, 1992) SQrikaisekikenkyQsho Kokyt]roku
- Y Ihara
Y. Ihara: On Fermat quotient and "the differentials of numbers". Algebraic analysis and number
theory (Kyoto, 1992). SQrikaisekikenkyQsho
Kokyt]roku, no. 810, pp. 324-341 (1992) (in
Japanese); (English transl, by S. Hahn with supplement ): the Univ. Georgia Preprint Series, no.
9, vol. 2, 16 pp (1994).