ON A TRIGONOMETRIC INEQUALITY OF VINOGRADOV

[摘要] The sum f(m, n) = SIGMA(a=1)m-1 (\sin(xan/m)\/sin(xa/m) arises in bounding incomplete exponential sums. In this article we show that for positive integers m, n with m > 1, f(m,n) < (4m/pi2)(log m + gamma + 1/8 - log(pi/2)) + (2/pi)(2-1/pi), where gamma is Euler's constant. This improves earlier bounds for f(m,n). (C) 1994 Academic Press, Inc.

[发布日期] 1994-12-01