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Concept

Square-free integer

Related publications (25)

Toroidal families and averages of L-functions, I

Philippe Michel

We initiate the study of certain families of L-functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values L( 2 1 , chi a )L( 21 , chi b ) for arbitrary ...

Polish Acad Sciences Inst Mathematics-Impan2024

Additive and geometric transversality of fractal sets in the integers

Florian Karl Richter

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

2024

On the Use of the Generalized Littlewood Theorem Concerning Integrals of the Logarithm of Analytical Functions for the Calculation of Infinite Sums and the Analysis of Zeroes of Analytical Functions

Serguei Sekatski

Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of an analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is applied to calcul ...

MDPI2023

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

The exploration process of critical Boltzmann planar maps decorated by a triangular O(n) loop model

Aleksandra Korzhenkova

In this paper we investigate pointed (q, g, n)-Boltzmann loop-decorated maps with loops traversing only inner triangular faces. Using peeling exploration Budd (2018) modified to this setting we show that its law in the non-generic critical phase can be cod ...

IMPA2022

Paths in pseudorandom graphs and applications

Van Thang Pham

Let G = (V, E) be an (n, d, lambda)-graph. In this paper, we give an asymptotically tight condition on the size of U subset of V such that the number of paths of length k in U is close to the expected number for arbitrary integer k >= 1. More precisely, we ...

CHARLES BABBAGE RES CTR2020

Minimal graphs for 2-factor extension

Dominique de Werra

Let G = (V, E) be a simple loopless finite undirected graph. We say that G is (2-factor) expandable if for any non-edge uv, G + uv has a 2-factor F that contains uv. We are interested in the following: Given a positive integer n = vertical bar V vertical b ...

ELSEVIER2020

A simple proof for a forbidden subposet problem

Abhishek Methuku

The poset Y-k,Y-2 consists of k + 2 distinct elements x(1), x(2), ..., x(k), y(1), y(2), such that x(1)

ELECTRONIC JOURNAL OF COMBINATORICS2020

Role of higher order plasmonic modes in one-dimensional nanogratings

Ershad Mohammadi, Foziyeh Sohrabi

By theoretically investigating the optical behavior of one-dimensional gold nanogratings using Fourier Modal Method, we have shown that both integer and non-integer multiples of surface plasmon polariton wavelengths should be taken into consideration in sp ...

SPRINGER2019

Forbidden induced subposets of given height

Istvan Tomon

Let P be a partially ordered set. The function La* (n, P) denotes the size of the largest family F subset of 2([n]) that does not contain an induced copy of P. It was proved by Methuku and Palvolgyi that there exists a constant C-P (depending only on P) su ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

The Bounded Cohomology of SL2 Over Local Fields and S-Integers

Nicolas Monod

It is proved that the continuous bounded cohomology of SL2(k) vanishes in all positive degrees whenever k is a non-Archimedean local field. This holds more generally for boundary-transitive groups of tree automorphisms and implies low degree vanishing for ...

OXFORD UNIV PRESS2019

Lonely Runner Polyhedra

Matthias Schymura

We study the Lonely Runner Conjecture, conceived by Jörg M. Wills in the 1960's: Given positive integers n_1, n_2, ... , n_k, there exists a positive real number t such that for all 1 \le j \le k the distance of t n_j to the nearest integer is at least 1 / ...

2019

Almost tiling of the Boolean lattice with copies of a poset

Istvan Tomon

Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and m ...

ELECTRONIC JOURNAL OF COMBINATORICS2018

On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Robert Granger

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

Elsevier2016

Cross-Intersecting Families of Vectors

János Pach

Given a sequence of positive integers , let denote the family of all sequences of positive integers such that for all . Two families of sequences (or vectors), , are said to be -cross-intersecting if no matter how we select and , there are at least distinc ...

Springer Japan Kk2015

Bounds for Pach's Selection Theorem and for the Minimum Solid Angle in a Simplex

Jan Kyncl

We estimate the selection constant in the following geometric selection theorem by Pach: For every positive integer d, there is a constant such that whenever are n-element subsets of , we can find a point and subsets for every , each of size at least , suc ...

Springer2015

Sound reasoning about integral data types with a reusable SMT solver interface

Viktor Kuncak, Régis William Blanc

We extend the Leon verification system for Scala with support for bit-vector reasoning, thus addressing one of its fundamental soundness limitation with respect to the treatment of integers primitives. We leverage significant progresses recently achieved i ...

ACM Press2015

Computing in social networks

Rachid Guerraoui, Anne-Marie Kermarrec, Kévin Clément Huguenin, Andrei Giurgiu

This paper defines the problem of Scalable Secure computing in a Social network: we call it the S-3 problem. In short, nodes, directly reflecting on associated users, need to compute a symmetric function f : V-n -> U of their inputs in a set of constant si ...

Elsevier2014

An extremal problem on crossing vectors

Bartosz Maria Walczak, Michal Lason

For positive integers w and k, two vectors A and B from Z(w) are called k-crossing if there are two coordinates i and j such that A[i] - B[i] >= k and B[j] - A[j] >= k. What is the maximum size of a family of pairwise 1-crossing and pairwise non-k-crossing ...

Academic Press Inc Elsevier Science2014