| dc.contributor.author | Alzer, H. | en |
| dc.contributor.author | Koumandos, S. | en |
| dc.creator | Alzer, H. | en |
| dc.creator | Koumandos, S. | en |
| dc.date.accessioned | 2019-12-02T10:33:33Z | |
| dc.date.available | 2019-12-02T10:33:33Z | |
| dc.date.issued | 2004 | |
| dc.identifier.issn | 0022-314X | |
| dc.identifier.uri | http://gnosis.library.ucy.ac.cy/handle/7/56413 | |
| dc.description.abstract | The trigonometric sum f(m, n) = ∑ k=1 m-1 sin(πkn/m) /sin(πk/m) (1 < m ∈ N, n ∈ N) has several applications in number theory. We prove that the mean value inequalities c1m(log m + γ - logπ/2) ≤ 1/m ∑ n=1 f(m, n) < c2m(log m + γ - logπ/2) (m = 2, 3,...) hold with the best possible constant factors c1 = 1/4[γ + log(4/π)] = 0.30533... and c 2 = 4/π2 = 0.40528... . This result refines and complements inequalities due to Cochrane, Peral, and Yu. © 2003 Elsevier Inc. All rights reserved. | en |
| dc.source | Journal of Number Theory | en |
| dc.source.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-1642526738&doi=10.1016%2fj.jnt.2003.10.003&partnerID=40&md5=c2a1b871b627395df63836c09f77a672 | |
| dc.subject | Inequalities | en |
| dc.subject | Arithmetic mean | en |
| dc.subject | Trigonometric sums | en |
| dc.title | On a trigonometric sum of Vinogradov | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.identifier.doi | 10.1016/j.jnt.2003.10.003 | |
| dc.description.volume | 105 | |
| dc.description.issue | 2 | |
| dc.description.startingpage | 251 | |
| dc.description.endingpage | 261 | |
| dc.author.faculty | Σχολή Θετικών και Εφαρμοσμένων Επιστημών / Faculty of Pure and Applied Sciences | |
| dc.author.department | Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics | |
| dc.type.uhtype | Article | en |
| dc.description.notes | <p>Cited By :3</p> | en |
| dc.source.abbreviation | J.Number Theory | en |
| dc.contributor.orcid | Koumandos, S. [0000-0002-3399-7471] | |
| dc.gnosis.orcid | 0000-0002-3399-7471 | |
