76 citations · 631 across the 35 of their papers we have counts for
5 papers · 2 filters
On accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function
Yaroslav D. Sergeyev
The Riemann Hypothesis has been of central interest to mathematicians for a long time and many unsuccessful attempts have been made to either prove or disprove it. Since the Rieman…
Counting systems and the First Hilbert problem
Yaroslav D. Sergeyev
The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to des…
Numerical point of view on Calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains
Yaroslav D. Sergeyev
The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with fu…
Evaluating the exact infinitesimal values of area of Sierpinski's carpet and volume of Menger's sponge
Yaroslav D. Sergeyev
Very often traditional approaches studying dynamics of self-similarity processes are not able to give their quantitative characteristics at infinity and, as a consequence, use limi…
A new applied approach for executing computations with infinite and infinitesimal quantities
Yaroslav D. Sergeyev
A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this paper. It is based on the principle `The part is less tha…