On an approach for evaluating certain trigonometric character sums using the discrete time heat kernel

Finite Trigonometric Character Sums via Discrete Fourier Analysis

We prove several old and new theorems about finite sums involving characters and trigonometric functions. These sums can be traced back to theta function identities from Ramanujan’s notebooks and were systematically first studied by Berndt and Zaharescu; their proofs involved complex contour integration. We show how to prove most of Berndt–Zaharescu’s and some new identities by elementary metho...

On Certain Character Sums over Smooth Numbers

the use of appropriate madm model for ranking the vendors of mci equipments using fuzzy approach

abstract nowadays, the science of decision making has been paid to more attention due to the complexity of the problems of suppliers selection. as known, one of the efficient tools in economic and human resources development is the extension of communication networks in developing countries. so, the proper selection of suppliers of tc equipments is of concern very much. in this study, a ...

On 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...

On Trigonometric Sums with Gaps

A well known theorem states as follows :' Let ni < n2 <. . ., nk+1 / nk > A > 1 be an infinite sequence of real numbers and S (ak + bk) a divergent series satisfying k=1 Then denotes the Lebesgue measure of the set in question. It seems likely that the Theorem remains true if it is not assumed that the n k are integers. On the other hand if nk ,f-n,.-1 is an arbitrary sequence of integers it is...