منابع مشابه
Positive trigonometric sums and applications
Some new positive trigonometric sums that sharpen Vietoris’s classical inequalities are presented. These sharp inequalities have remarkable applications in geometric function theory. In particular, we obtain information for the partial sums of certain analytic functions that correspond to starlike functions in the unit disk. We also survey some earlier results with additional remarks and comments.
متن کاملSome Notes on Trigonometric Sums
1 Trigonometric Sums 1 1.1 Gauss Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Kloosterman Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Geometrization 2 2.1 A Lemma on Torsors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Artin-Shreier Sheaves . . . . . . . . . . . . . . . . . ...
متن کاملSome Results on Gauss Sums
is again a Dirichlet character modulo n. In fact, the set of Dirichlet characters modulo n is again a multiplicative group, called the dual group of (Z/nZ)× and denoted ̂ (Z/nZ)×. The identity element of the dual group, mapping every element of (Z/nZ)× to 1, is the trivial character modulo n, denoted 1n or just 1 when n is clear, Since (Z/nZ)× is a finite group the values taken by any Dirichlet ...
متن کاملFactors of Some Binomials Sums
We confirm several conjectures of Guo, Jouhet and Zeng concerning the factors of some binomials sums.
متن کاملOn Some Trigonometric Power Sums
In contrast to Fourier series, these finite power sums are over the angles equally dividing the upper-half plane. Moreover, these beautiful and somewhat surprising sums often arise in analysis. In this note, we extend the above results to the power sums as shown in identities (17), (19), (25), (26), (32), (33), (34), (35), and (36) and in the appendix. The method is based on the generating func...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2003
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(02)00884-1