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Euler-Zagier Sums Via Trigonometric Series
(Publishing House of the Romanian Academy, 2023) Çam Çelik, Şermin; 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.
A Note on Points on Algebraic Sets
(Hacettepe Üniversitesi, 2021) Çam Çelik, Şermin; Göral, Haydar
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. Yoruk, Statistics and characterization of matrices by determinant and trace, Ramanujan J., 2019] and also anwers some questions from the same article.

Mathematics / Matematik