{"docId":1356,"paperId":1356,"url":"https:\/\/hrj.episciences.org\/1356","doi":"10.46298\/hrj.2014.1356","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":48,"name":"Volume 38 - 2015"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01254038","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01254038v1","dateSubmitted":"2016-01-14 16:06:27","dateAccepted":"2016-01-14 16:06:27","datePublished":"2014-01-01 08:00:00","titles":{"en":"On congruences for certain sums of E. Lehmer's type"},"authors":["Kanemitsu, Shigeru","Kuzumaki, Takako","Urbanowicz, Jerzy"],"abstracts":{"en":"Let n > 1 be an odd natural number and let r (1 < r < n) be a natural number relatively prime to n. Denote by \u03c7n the principal character modulo n. In Section 3 we prove some new congruences for the sums T r,k (n) = n r ] i=1 (\u03c7n(i) i k) (mod n s+1) for s \u2208 {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"},"keywords":[{"en":"Congruence"},{"en":"generalized Bernoulli number"},{"en":"special value of L-function"},{"en":"ordinary Bernoulli number"},{"en":"Bernoulli polyno- mial"},{"en":"Euler number"},"2010 Mathematics Subject Classification. primary 11B68; secondary 11R42, 11A07","[MATH] Mathematics [math]"]}