Results 151 to 160 of about 6,205 (243)

On moments of the derivative of CUE characteristic polynomials and the Riemann zeta function

open access: yesJournal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract We study the derivative of the characteristic polynomial of N×N$N \times N$ Haar‐distributed unitary matrices. We obtain new explicit formulae for complex‐valued moments when the spectral variable is inside the unit disc, in the limit N→∞$N \rightarrow \infty$.
Nicholas Simm, Fei Wei
wiley   +1 more source

Riemann’s method in the theory of special functions [PDF]

open access: yesBulletin of the American Mathematical Society, 1956
openaire   +2 more sources

Unitary ensembles with a critical edge point, their multiplicative statistics, and the Korteweg‐de‐Vries hierarchy

open access: yesJournal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract We study the multiplicative statistics associated to the limiting determinantal point process describing eigenvalues of unitary random matrices with a critical edge point, where the limiting eigenvalue density vanishes like a power 5/2. We prove that these statistics are governed by the first three equations of the Korteweg‐de‐Vries (KdV ...
Mattia Cafasso   +1 more
wiley   +1 more source

Discrete analogues of second‐order Riesz transforms

open access: yesJournal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract Discrete analogues of classical operators in harmonic analysis have been widely studied, revealing deep connections with areas such as ergodic theory and analytic number theory. This line of research is commonly known as Discrete Analogues in Harmonic Analysis (DAHA).
Rodrigo Bañuelos, Daesung Kim
wiley   +1 more source

Diophantine tuples and product sets in shifted powers

open access: yesJournal 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

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