THÉORIE DES NOMBRES BESANÇON
Années 1992/93-1993/94
Corrigendum to the paper
"On some new congruences between generalized Bernoulli numbers, II"
(Publ. Math. Fac. Sci. Besançon (Théorie des Nombres) Années 1989/90 - 1990/91)
J. URBANOWICZ
Corrigendum to the paper
"On some new congruences between generalized Bernoulli numbers, II"
(Publ. Math. Fac. Sci. Besançon (théorie des nombres), Années 1989/90-1990/91)
Jerzy Urbanowicz Institute of Mathematics Polish Academy of Sciences
ul. Sniadeckich 8 00-950 Warszawa, Poland
The end of the proof of Lemma 6 should be corrected. Lines from 13 to the end of page 17 should read:
"Thus in view of
ç , ç _ / * o ( < * / 4 ) , if 4 II d,
1 + 4 \ 2t0(d/4, a = ± 3 (mod 8)) if 8 | d,
and
( ) s s _ ( -toW), if 4 || d,
[ J °2 + °3 ~ \ -2t0(d/4, a = ± 1 (mod 8)), if 8 | d,
we obtain
(**) t0(S, a = ± 3 (mod 8)) = 0.
Therefore (3.27) implies
tk = \ t 2 (mod 2o r d 2 k + 6) , and by Lemma 2, the lemma follows." •
As for détails, (*) follows from
d \ ( d \ f d\
(5/2 + ay \ê/2 — a J \a J
(which holds for 0 < a < 6/4: in ail the cases), and (**) is a conséquence of
t0(d/4,a = ±3 (mod 8)) = t0(d/4, a = ± 1 (mod 8)) = t0(d/8, a = -6* (mod 4)) (which holds for d = ±8d*).
