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Concept

Prime number theorem

Related publications (21)

Non-planarity of Markoff graphs mod p

Matthew De Courcy-Ireland

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

European Mathematical Soc-Ems2024

The double exponential runtime is tight for 2-stage stochastic ILPs

Kim-Manuel Klein, Alexandra Anna Lassota

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...

SPRINGER HEIDELBERG2022

Safety in Numbers: Asymptotic Analysis of a Monitoring Problem

Emre Telatar, Reka Inovan

In this work, we introduce a setup where a monitoring entity attempts to distinguish a cheating player among a group of regular players where all players behave in order to maximize their reward. We assume that the cheating player has an "information advan ...

IEEE2022

Demography of galactic technosignatures

Claudio Grimaldi

Probabilistic arguments about the existence of technological life beyond Earth traditionally refer to the Drake equation to draw possible estimates of the number of technologically advanced civilizations releasing, either intentionally or not, electromagne ...

OXFORD UNIV PRESS2021

Probabilistic and deterministic full field approaches to simulate recrystallization in ODS steels

Roland Logé

Mechanical and functional properties of Oxide Dispersion Strengthened (ODS) ferritic/martensitic steels are strongly related to their microstructures. Thus, numerical modeling of microstructure evolution during ODS forming is of prime importance. In this w ...

ELSEVIER2020

A class of 2-local finite spectra which admit a v1/2-self-map

Philip Egger

At the prime 2, Behrens, Hill, Hopkins and Mahowald showed that M-2 (1, 4) admits a 32-periodic v(2)-self-map. More recently, in joint work with Mahowald, we showed that A(1) also admits a 32-periodic v(2)-self-map. This leads to the question of whether th ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

A PRACTICAL ANALYTIC METHOD FOR CALCULATING pi(x)

Thorsten Kleinjung

In this paper we give a description of a practical analytic method for the computation of pi(x), the number of prime numbers

American Mathematical Society2017

Universal p'-central extensions

Jacques Thévenaz, Caroline Lassueur

It is well-known that a finite group possesses a universal central extension if and only if it is a perfect group. Similarly, given a prime number p, we show that a finite group possesses a universal p′-central extension if and only if the p′-part of its a ...

Elsevier2017

Some consequences of Masser's counting theorem on elliptic curves

We use Masser's counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser's result with bounds on the rank and torsion of ...

Springer Heidelberg2017

Isogeny graphs of ordinary abelian varieties

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

Sign changes of Kloosterman sums with almost prime moduli

Ping Xi

We prove that the Kloosterman sum changes sign infinitely often as runs over squarefree moduli with at most 10 prime factors, which improves the previous results of Fouvry and Michel, Sivak-Fischler and Matomaki, replacing 10 by 23, 18 and 15, respectively ...

Springer Verlag2015

On The Exponent Of Distribution Of The Ternary Divisor Function

Philippe Michel

We show that the exponent of distribution of the ternary divisor function d(3) in arithmetic progressions to prime moduli is at least 1/2 + 1/46, improving results of Friedlander-Iwaniec and Heath-Brown. Furthermore, when averaging over a fixed residue cla ...

London Mathematical Society, Cambridge2015

Prime Power Terms In Elliptic Divisibility Sequences

We study a problem on specializations of multiples of rational points on elliptic curves analogous to the Mersenne problem. We solve this problem when descent via isogeny is possible by giving explicit bounds on the indices of prime power terms in elliptic ...

American Mathematical Society2014

Some applications of the Weil-Barner explicit formula

Thorsten Kleinjung

The Weil-Barner explicit formula is applied to the prime counting function and to the problem of numerical partial verification of the Riemann hypothesis. ...

Wiley-V C H Verlag Gmbh2013

The functor of p-permutation modules for abelian groups

Mélanie Baumann

Let k be a field of characteristic p, where p is a prime number, let pp_k(G) be the Grothendieck group of p-permutation kG-modules, where G is a finite group, and let Cpp_k(G) be pp_k(G) tensored with the field of complex numbers C. In this article, we fin ...

Elsevier2013

On the size of Satake parameters for unitary cuspidal automorphic representations for GL(4)

Nahid Walji

Let Pi be a cuspidal automorphic representation for GL(4) over a number field F. We obtain unconditional lower bounds on the number of places at which the Satake parameters are not "too large". In the case of self-dual Pi with non-trivial central character ...

Academic Press Inc Elsevier Science2013

Primeless Factoring-Based Cryptography

Serge Vaudenay, Sonia Mihaela Bogos, Ioana Cristina Carlson

Factoring-based public-key cryptosystems have an overall complexity which is dominated by the key-production algorithm, which requires the generation of prime numbers. This is most inconvenient in settings where the key-generation is not an one-off process ...

2013

Le foncteur de bi-ensembles des modules de p-permutation

Mélanie Baumann

Let k be an algebraically closed field of characteristic p, where p is a prime number or 0. Let G be a finite group and ppk(G) be the Grothendieck group of p-permutation kG-modules. If we tensor it with C, then Cppk becomes a C-linear biset functor. Recall ...

EPFL2012

Primeless Modular Cryptography (Extended Abstract)

Serge Vaudenay, Sonia Mihaela Bogos, Ioana Cristina Carlson

Most of the known public-key cryptosystems have an overall complexity which is dominated by the key-production algorithm, which requires the generation of prime numbers. This is most inconvenient in settings where the key-generation is not an one-off proce ...

2012

Relative Projectivity and Relative Endotrivial Modules

Caroline Lassueur

This dissertation is concerned with modular representation theory of finite groups, and more precisely, with the study of classes of representations, which we shall term relative endotrivial modules. Given a prime number p, a finite group G of order divisi ...

EPFL2012

Related publications (21)

American Mathematical Society2017

Wiley-V C H Verlag Gmbh2013