Results 41 to 50 of about 7,736 (165)

Tian’s Conjecture on the Prime Factorization of the Binomial Coefficient $\mathbf{\left(}{\displaystyle \genfrac{}{}{0pt}{}{\mathit{n}\mathbf{+}\mathbf{1}}{\mathbf{2}}}\mathbf{\right)}$

Mathematics
Tian’s conjecture states that for any fixed distinct prime numbers p1,…,pm, the Diophantine equation n+12=p1α1·p2α2···pmαm in positive integers n,α1,…,αm has at most m solutions.
Zhenbing Zeng, Ákos Pintér, Xinchu Fu, Jianjun Paul Tian   +3 more
doaj   +1 more source

Positivity Problems for Low-Order Linear Recurrence Sequences

, 2013
We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem} (are all but finitely many terms of a given LRS ...
Ouaknine, Joel, Worrell, James
core   +1 more source

Diophantine tuples and product sets in shifted powers

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract Let k⩾2$k\geqslant 2$ and n≠0$n\ne 0$. A Diophantine tuple with property Dk(n)$D_k(n)$ is a set of positive integers A$A$ such that ab+n$ab+n$ is a k$k$th power for all a,b∈A$a,b\in A$ with a≠b$a\ne b$. Such generalizations of classical Diophantine tuples have been studied extensively.
Ernie Croot, Chi Hoi Yip
wiley   +1 more source

C/C++ implementation of functions of the class LT0 [PDF]

, 2000
This report describes an on-going implementation, in C/C++, of the functions and schemes of the formal system LT0, presented in the paper Caporaso, Pani and Covino [1].
Calude, Elena, Kay, Peter, Luo, Weiwei
core  

A universal example for quantitative semi‐uniform stability

Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.
Abstract We characterise quantitative semi‐uniform stability for C0$C_0$‐semigroups arising from port‐Hamiltonian systems, complementing recent works on exponential and strong stability. With the result, we present a simple universal example class of port‐Hamiltonian C0$C_0$‐semigroups exhibiting arbitrary decay rates slower than t−1/2$t^{-1/2}$.
Sahiba Arora, Felix L. Schwenninger, Ingrid Vukusic, Marcus Waurick   +3 more
wiley   +1 more source

Plank theorems and their applications: A survey

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
William Verreault
wiley   +1 more source

The Davenport–Heilbronn method: 80 years on

Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.
Abstract The Davenport–Heilbronn method is a version of the circle method that was developed for studying Diophantine inequalities in the paper (Davenport and Heilbronn, J. Lond. Math. Soc. (1) 21 (1946), 185–193). We discuss the main ideas in the paper, together with an account of the development of the subject in the intervening 80 years.
Tim Browning
wiley   +1 more source

On a conjecture on exponential Diophantine equations [PDF]

Acta Arithmetica, 2009
We study the solutions of a Diophantine equation of the form $a^x+b^y=c^z$, where $a\equiv 2 \pmod 4$, $b\equiv 3 \pmod 4$ and $\gcd (a,b,c)=1$. The main result is that if there exists a solution $(x,y,z)=(2,2,r)$ with $r>1$ odd then this is the only solution in integers greater than 1, with the possible exception of finitely many values $(c,r)$. We
Cipu, Mihai, Mignotte, Maurice
openaire   +2 more sources

Figurate primes and Hilbert's 8th problem

, 2014
In this paper, by using the theory of elliptic curves, we discuss several Diophantine equations related with the so-called figurate primes. Meanwhile, we raise several conjectures related with figurate primes and Hilbert's 8th problem, including Goldbach'
Cai, Tianxin, Shen, Zhongyan, Zhang, Yong   +2 more
core   +1 more source

The dimension of well approximable numbers

Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.
Abstract In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine ...
Victor Beresnevich, Sanju Velani
wiley   +1 more source