Results 111 to 120 of about 2,483 (259)
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract We survey ideas surrounding the study of the number of integers that can be represented as the sum of three positive cubes. We focus on the early contribution of Davenport using elementary techniques, and the subsequent developments due to Vaughan, which introduced Fourier analysis and mirrored many of the important developments of the Hardy ...
James Maynard
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PKCHD: Towards a Probabilistic Knapsack Public-Key Cryptosystem with High Density
Information, 2019 By introducing an easy knapsack-type problem, a probabilistic knapsack-type public key cryptosystem (PKCHD) is proposed. It uses a Chinese remainder theorem to disguise the easy knapsack sequence. Thence, to recover the trapdoor information, the implicit
Yuan Ping +4 more
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Simultaneous diophantine approximation [PDF]
Bulletin of the Australian Mathematical Society, 1972 AbstractUsing a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — αr)2 < c, r(q — βr)2 < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals α and β, provided that c > 1/2.6394.
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Random Diophantine equations in the primes II
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract Let d⩾2$d\geqslant 2$ and n⩾d$n\geqslant d$ with (d,n)∉{(2,2),(3,3)}$(d,n)\notin \lbrace (2,2),(3,3)\rbrace$. We consider homogeneous Diophantine equations of degree d$d$ in n+1$n+1$ variables and whether they have solutions in the primes.
Philippa Holdridge
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Diophantine Approximation and Dynamical Systems
, 2020 The subject of diophantine approximation is a classical mathematic problem, as old as it is well studied. There are many different texts describing its connection to more modern areas of study, but few which do so with the aim of exploring the ...
Lee, Antony
core
Diophantine approximations and convergence of series in Banach spaces
Le Matematiche, 1993 n this paper we give a new proof of a known diophantine approximation result, then we apply this to prove convergence of a class of series in a Banach space, whose terms are defined recursively.
Giovanni Fiorito +2 more
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Asymptotic Diophantine Approximations to E [PDF]
Proceedings of the National Academy of Sciences, 1966 —Schmidt5 proved that for almost all real numbers α, the number of solutions in integers p, q of the inequalities $$ \left| {q\alpha - p} \right| < 1/qand1\underline \leqslant q\underline \leqslant B$$ is asymptotic to a constant times log B. One might conjecture that the classical numbers (e.g., algebraic numbers, e, π) behave like almost all ...
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Solving the n $n$‐Player Tullock Contest
Journal of Public Economic Theory, Volume 28, Issue 2, April 2026.ABSTRACT The n $n$‐player Tullock contest with complete information is known to admit explicit solutions in special cases, such as (i) homogeneous valuations, (ii) constant returns, and (iii) two contestants. But can the model be solved more generally?
Christian Ewerhart
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Karpatsʹkì Matematičnì Publìkacìï, 2019 Algebraic and recursion equations are widely used in different areas of mathematics, so various objects and methods of research that are associated with them are very important.
I.I. Lishchynsky
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GCD inequalities arising from codimension‐2 blowups
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract Assuming a deep Diophantine geometry conjecture by Vojta, Silverman proved an inequality giving an upper bound for the greatest common divisor (GCD). In this paper, we unconditionally prove a weaker version of this inequality. The main ingredient is the Ru–Vojta theory, which provides an efficient method of using Schmidt subspace theorem.
Yu Yasufuku
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