A. Mosunov

activity

20132022

most citedNumerical and Statistical Analysis of Aliquot Sequences

7 citations · 10 across the 10 of their papers we have counts for

collaborators

10 papers

math.NT2022

A Lower Bound for the Area of the Fundamental Region of a Binary Form

Jason Fang, Anton Mosunov

Let $F (x, y) = k = 0 \prod n - 1 (δ_{k} x - γ_{k} y)$ be a binary form of degree $n \geq 1$ , with complex coefficients, written as a product of $n$ linear forms in $\mathbb…

math.NT2022

Absolute Bound On the Number of Solutions of Certain Diophantine Equations of Thue and Thue-Mahler Type

Anton Mosunov

Let $F \in Z [x, y]$ be an irreducible binary form of degree $d \geq 7$ and content one. Let $α$ be a root of $F (x, 1)$ and assume that the field extension $\mathbb Q(α)/\ma…

math.NT2021

On the Generalization of the Gap Principle

Anton Mosunov

Let $α$ be a real algebraic number of degree $d \geq 3$ and let $β \in Q (α)$ be irrational. Let $μ$ be a real number such that $(d /2) + 1 < μ < d$ and let $C_{0}$ be a positive…

math.NT2021★ 7 cited

Numerical and Statistical Analysis of Aliquot Sequences

Kevin Chum, Richard K. Guy, Michael J. Jacobson +1

We present a variety of numerical data related to the growth of terms in aliquot sequences, iterations of the function $s (n) = σ (n) - n$ . First, we compute the geometric mean of th…

math.NT2021

On the Representation of Integers by Binary Forms Defined by Means of the Relation $(x + y i)^{n} = R_{n} (x, y) + J_{n} (x, y) i$

A. Mosunov

Let $F$ be a binary form with integer coefficients, non-zero discriminant and degree $d \geq 3$ . Let $R_{F} (Z)$ denote the number of integers of absolute value at most $Z$ which are…

math.NT2021

On the Automorphism Group of a Binary Form Associated with Algebraic Trigonometric Quantities

Anton Mosunov

Let $F (x, y)$ be a binary form of degree at least three and non-zero discriminant. In this article we compute the automorphism group $Aut F$ for four families of bin…

math.NT2020★ 3 cited

On the Area of the Fundamental Region of a Binary Form Associated with Algebraic Trigonometric Quantities

Anton Mosunov

Let $F (x, y)$ be a binary form of degree at least three and non-zero discriminant. We estimate the area $A_{F}$ bounded by the curve $∣ F (x, y) ∣ = 1$ for four families of binary forms…

math.NT2020

On the Area Bounded by the Curve $\prod_{k = 1}^{n} ∣ x sin (k π / n) - y cos (k π / n) ∣ = 1$

Anton Mosunov

For a positive integer $n$ , let $F_{n}^{*} (X, Y) = k = 1 \prod n (X sin (\frac{k π}{n}) - Y cos (\frac{k π}{n})) .$ In 2000 Bean and Laugesen pro…

math.NT2015

Unconditional Class Group Tabulation of Imaginary Quadratic Fields to $∣Δ∣ < 2^{40}$

A. S. Mosunov, M. J. Jacobson

We present an improved algorithm for tabulating class groups of imaginary quadratic fields of bounded discriminant. Our method uses classical class number formulas involving theta-…

math.NT2013

Ideal Class Group Algorithms in the Ring of Integral Quaternions

Anton S. Mosunov

An ideal is a classical object of study in the field of algebraic number theory. In maximal quadratic orders of number fields, ideals usually represented by the $Z$ -basis.…

A Lower Bound for the Area of the Fundamental Region of a Binary Form

Absolute Bound On the Number of Solutions of Certain Diophantine Equations of Thue and Thue-Mahler Type

On the Generalization of the Gap Principle

Numerical and Statistical Analysis of Aliquot Sequences

On the Representation of Integers by Binary Forms Defined by Means of the Relation (x+yi)n=Rn​(x,y)+Jn​(x,y)i

On the Automorphism Group of a Binary Form Associated with Algebraic Trigonometric Quantities

On the Area of the Fundamental Region of a Binary Form Associated with Algebraic Trigonometric Quantities

On the Area Bounded by the Curve ∏k=1n​∣xsin(kπ/n)−ycos(kπ/n)∣=1

Unconditional Class Group Tabulation of Imaginary Quadratic Fields to ∣Δ∣<240

Ideal Class Group Algorithms in the Ring of Integral Quaternions

On the Representation of Integers by Binary Forms Defined by Means of the Relation $(x + y i)^{n} = R_{n} (x, y) + J_{n} (x, y) i$

On the Area Bounded by the Curve $\prod_{k = 1}^{n} ∣ x sin (k π / n) - y cos (k π / n) ∣ = 1$

Unconditional Class Group Tabulation of Imaginary Quadratic Fields to $∣Δ∣ < 2^{40}$