TY - JOUR
T1 - Fractional parts and their relations to the values of the Riemann zeta function
AU - Alabdulmohsin, Ibrahim
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2017/9/6
Y1 - 2017/9/6
N2 - A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.
AB - A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.
UR - http://hdl.handle.net/10754/625492
UR - https://link.springer.com/article/10.1007%2Fs40065-017-0184-2
UR - http://www.scopus.com/inward/record.url?scp=85081340302&partnerID=8YFLogxK
U2 - 10.1007/s40065-017-0184-2
DO - 10.1007/s40065-017-0184-2
M3 - Article
SN - 2193-5343
VL - 7
SP - 1
EP - 8
JO - Arabian Journal of Mathematics
JF - Arabian Journal of Mathematics
IS - 1
ER -