On a Trigonometric Inequality of Vinogradov
β Scribed by K.T. Yu
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 143 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0022-314X
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π SIMILAR VOLUMES
The trigonometric sum f Γ°m; nΓ ΒΌ X mΓ1 kΒΌ1 j sinΓ°pkn=mΓj sinΓ°pk=mΓ Γ°1omAN; nANΓ has several applications in number theory. We prove that the mean value inequalities ΒΌ 2; 3; yΓ hold with the best possible constant factors This result refines and complements inequalities due to Cochrane, Peral, and
We obtain a representation formula for the trigonometric sum f (m, n) and deduce from it the upper bound f(m, n) < (4/p 2 ) m log m+ (4/p 2 )(c -log(p/2)+2C G ) m+O(m/`log m), where C G is the supremum of the function G(t) :=; . k=1 log |2 sin pkt|/(4k 2 -1), over the set of irrationals. The coeffi