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    A note on points on algebraic sets
    (Hacettepe Journal of Mathematics and Statistics, 2021) Çelik, Şermin Çam
    ABSTRACT: In this short note, we count the points on algebraic sets which lie in a subset of a domain. It is proved that the set of points on algebraic sets coming from certain subsets of a domain has the full asymptotic. This generalizes the first theorem of [E. Alkan and E.S. Yörük, Statistics and characterization of matrices by determinant and trace, Ramanujan J., 2019] and also anwers some questions from the same article.
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    EULER–ZAGIER SUMS VIA TRIGONOMETRIC SERIES
    (Publishing House of the Romanian Academy, 2023) Çelik, Şermin Çam; Göral, Haydar
    In this note, we study the evaluations of Euler sums via trigonometric series. It is a commonly believed conjecture that for an even weight greater than seven, Euler sums cannot be evaluated in terms of the special values of the Riemann zeta function. For an even weight, we reduce the evaluations of Euler sums into the evaluations of double series and integrals of products of Clausen functions. We also re-evaluate Euler sums of odd weight using a new method based on trigonometric series. © 2023 Editura Academiei Romane. All rights reserved.