Random Diophantine equations in the primes
Mathematika, Volume 72, Issue 3, July 2026.Abstract We consider equations of the form a1x1k+⋯+asxsk=0$a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}=0$ where the variables xi$x_{i}$ are all taken to be primes. We define an analogue of the Hasse principle for solubility in the primes (which we call the prime Hasse principle), and prove that, whenever k⩾2$k\geqslant 2$, s⩾3k+2$s\geqslant 3k+2$, this holds
Philippa Holdridge
wiley +1 more source
On the infinite divisibility of the ratio of two gamma-distributed variables
, 1978 It is shown that the distribution of the ratio of two independent gamma-distributed random variables is infinitely divisible. This result provides a solution to an unsolved problem given by F. W.
Goovaerts, M.J. +2 more
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Quantitative asymptotics for polynomial patterns in the primes
Mathematika, Volume 72, Issue 3, July 2026.Abstract We prove quantitative estimates for averages of the von Mangoldt and Möbius functions along polynomial progressions n+P1(m),…,n+Pk(m)$n+P_1(m),\ldots, n+P_k(m)$ for a large class of polynomials Pi$P_i$. The error terms obtained save an arbitrary power of logarithm, matching the classical Siegel–Walfisz error term.
Lilian Matthiesen +2 more
wiley +1 more source
Some recent results in infinite divisibility
In this paper, a survey is given of some recent developments in infinite divisibility. There are three main topics: (i) the occurrence of infinitely divisible distributions in applied stochastic processes such as queueing processes and birth-death ...
Steutel, F. W.
core
Some new results of infinite divisibility on the half-line
, 2015 Cette thèse donne de nouveaux résultats de lois infiniment divisibles. La résolution d'une conjecture de Steutel (1973) à propos de la divisibilité infinie des puissances d'une variable gamma, et d'une conjecture de Bondesson (1992) à propos de la ...
Bosch, Pierre
core
In-Wheel Motor Fault Diagnosis Using Affinity Propagation Minimum-Distance Discriminant Projection and Weibull-Kernel-Function-Based SVDD. [PDF]
Sensors (Basel), 2023 Liu B, Xue H, Ding D, Sun N, Chen P.
europepmc +1 more source
Aspects of Randomization in Infinitely Divisible and Max-Infinitely Divisible Laws
, 2003 Continuing the study reported in Satheesh (2001),(arXiv:math.PR/0304499 dated 01May2003) here we study certain aspects of randomization in infinitely divisible (ID) and max-infinitely divisible (MID) laws. They generalize ID and MID laws. In particular we study mixtures of ID & MID laws, its relation to random sums & random maximums ...
openaire +2 more sources
Infinite divisibility of random variables and their integer parts
It is examined to what extent the infinite divisibility of a random variable X entails the infinite divisibility of its integer part [X] or vice versa.
Bondesson, Lennart +2 more
core
Algebras, Graphs and Ordered Sets - ALGOS 2020 & the Mathematical Contributions of Maurice Pouzet. [PDF]
Order (Dordr), 2023 Couceiro M, Duffus D.
europepmc +1 more source
Infinite divisibility of sub-stable processes. Part I. geometry of sub-spaces of Lα-space
, 1995 Generalizing the definition of sub-Gaussian processes we define a sub-stable process as a scale mixture of symmetric stable processes and study its infinite divisibility.
Misiewicz, Jolanta K.
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