On a monotonic trigonometric sum
โ Scribed by Gavin Brown; Stamatis Koumandos
- Publisher
- Springer Vienna
- Year
- 1997
- Tongue
- English
- Weight
- 317 KB
- Volume
- 123
- Category
- Article
- ISSN
- 0026-9255
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๐ SIMILAR VOLUMES
The trigonometric sum f รฐm; nร ยผ X mร1 kยผ1 j sinรฐpkn=mรj sinรฐpk=mร รฐ1omAN; nANร has several applications in number theory. We prove that the mean value inequalities ยผ 2; 3; yร hold with the best possible constant factors This result refines and complements inequalities due to Cochrane, Peral, and
By numerical experiments they were led to conjecture The first published solution by J. Boersma and P. J. DeDoelder 1 confirms the first conjecture and disproves the second one numerically. Their proof has been criticized by several authors, since it ignores all w x questions of convergence. In 2 ,