arXiv subjects

L. Tóth

Publications and source records attributed to L. Tóth.

3 recordsLinked to original sources

arXiv2021

Mean values of multivariable multiplicative functions and applications to the average number of cyclic subgroups and multivariable averages associated with the LCM function

We use multiple zeta functions to prove, under suitable assumptions, precise asymptotic formulas for the averages of multivariable multiplicative functions. As applications, we prove some conjectures on the average number of cyclic subgroups of the group ${\mathbb Z}_{m_1}\times\dots\times {\mathbb Z}_{m_n}$ and multivariable averages associated with the LCM function.

math.NT↗

arXiv2019

Coefficients of (inverse) unitary cyclotomic polynomials

The notion of block divisibility naturally leads one to introduce unitary cyclotomic polynomials $Φ_n^*(x)$. They can be written as certain products of cyclotomic poynomials. We study the case where $n$ has two or three distinct prime factors using numerical semigroups, respectively Bachman's inclusion-exclusion polynomials. Given $m\ge 1$ we show that every integer occurs as a coefficient of $Φ^*_{mn}(x)$ for some $n\ge 1$. Here $n$ will typically have many different prime factors. We also consider similar questions for the polynomials $(x^n-1)/Φ_n^*(x),$ the inverse unitary cyclotomic polynomials.

math.NT↗

arXiv2014

Spectroellipsometric and ion beam analytical studies on a glazed ceramic object with metallic lustre decoration

In this work recently produced and commercially available glazed ceramic object with metallic lustre decoration was studied by using a spectroscopic ellipsometer with rotating compensator. The thickness and metal content of the surface lustre layers are determined by ion beam analytical techniques, i.e., Rutherford backscattering spectrometry and external beam particle-induced X-ray emission and the results were utilized in the construction of multilayer optical models for the evaluation and interpretation of the spectroellipsometric measurements.

cond-mat.mtrl-sci↗