eng
episciences.org
Hardy-Ramanujan Journal
2804-7370
2014-01-01
Volume 38 - 2015
10.46298/hrj.2014.1356
1356
journal article
On congruences for certain sums of E. Lehmer's type
Shigeru Kanemitsu
Takako Kuzumaki
Jerzy Urbanowicz
Let n > 1 be an odd natural number and let r (1 < r < n) be a natural number relatively prime to n. Denote by χn the principal character modulo n. In Section 3 we prove some new congruences for the sums T r,k (n) = n r ] i=1 (χn(i) i k) (mod n s+1) for s ∈ {0, 1, 2}, for all divisors r of 24 and for some natural numbers k.We obtain 82 new congruences for T r,k (n), which generalize those obtained in [Ler05], [Leh38] and [Sun08] if n = p is an odd prime. Section 4 is an appendix by the second and third named authors. It contains some new congruences for the sums Ur(n) = n
https://hrj.episciences.org/1356/pdf
Congruence
generalized Bernoulli number
special value of L-function
ordinary Bernoulli number
Bernoulli polyno- mial
Euler number
2010 Mathematics Subject Classification. primary 11B68; secondary 11R42, 11A07
[MATH] Mathematics [math]