Dirk Zeindler

activity

20092026

most citedOn the number of cycles in a random permutation

18 citations · 88 across the 20 of their papers we have counts for

collaborators

24 papers

math.NT2026

On the exponential sum over squarefree integers

Nicolas Robles, Alexandru Zaharescu, Dirk Zeindler

Let $μ$ be the Möbius function and $e (t) = e^{2 π i t}$ . We prove that if $N \geq 2$ , $α \in R$ , $(a, q) = 1$ , and $∣ α - a / q ∣ \leq q^{- 2}$ , then \[\bigg|\sum_{n\le N}μ^2(n)e(αn)\bigg|\ll\l…

math.NT2026

Bilinear forms with Kloosterman fractions and applications

Anji Dong, Nicolas Robles, Dirk Zeindler

We establish improved bounds for bilinear forms with Kloosterman fractions of the form $\sum\sum_{m, n} α_{m} β_{n} e (a m / (bn))$ with $M < m \leq 2 M$ , $N < n \leq 2 N$ and $(m,n)=…

math.NT2024

Exponential sums twisted by general arithmetic functions

Anji Dong, Nicolas Robles, Alexandru Zaharescu +1

We examine exponential sums of the form $\sum_{n \leq X} w (n) e^{2 π i α n^{k}}$ , for $k = 1, 2$ , where $α$ satisfies a generalized Diophantine approximation and where $w$ are different arit…

math.NT2024

Strange and pseudo-differentiable functions with applications to prime partitions

Anji Dong, Nicolas Robles, Alexandru Zaharescu +1

Let $p_{P_{r}} (n)$ denote the number of partitions of $n$ into $r$ -full primes. We use the Hardy-Littlewood circle method to find the asymptotic of $\mathfrak{p}_…

math.NT2022★ 1 cited

Partitions into semiprimes

Madhuparna Das, Nicolas Robles, Alexandru Zaharescu +1

Let $P$ denote the set of primes and $N \subset N$ be a set with arbitrary weights attached to its elements. Set $p_{N} (n)$ to be th…

math.PR2020

Precise asymptotics of longest cycles in random permutations without macroscopic cycles

Volker Betz, Julian Mühlbauer, Helge Schäfer +1

We consider Ewens random permutations of length $n$ conditioned to have no cycle longer than $n^{β}$ with $0 < β < 1$ and to study the asymptotic behaviour as $n \to \infty$ . We obtain ver…

math.PR2019

Long cycle of random permutations with polynomially growing cycle weights

Dirk Zeindler

We study the asymptotic behavior of the long cycles of a random permutation of $n$ objects with respect to multiplicative measures with polynomial growing cycle weights. We show th…

math.PR2018

Random permutations with logarithmic cycle weights

Nicolas Robles, Dirk Zeindler

We consider random permutations on $\Sn$ with logarithmic growing cycles weights and study asymptotic behavior as the length $n$ tends to infinity. We show that the cycle count pro…

math.NT2018★ 1 cited

More than five-twelfths of the zeros of $ζ$ are on the critical line

Kyle Pratt, Nicolas Robles, Alexandru Zaharescu +1

The second moment of the Riemann zeta-function twisted by a normalized Dirichlet polynomial with coefficients of the form $(μ\star Λ_1^{\star k_1} \star Λ_2^{\star k_2} \star \cdot…

math.PR2017

Random permutations without macroscopic cycles

Volker Betz, Helge Schäfer, Dirk Zeindler

We consider uniform random permutations of length $n$ conditioned to have no cycle longer than $n^{β}$ with $0 < β < 1$ , in the limit of large $n$ . Since in unconstrained uniform random…

math.NT2016

On mean values of mollifiers and L-functions associated to primitive cusp forms

Patrick Kühn, Nicolas Robles, Dirk Zeindler

We study the second moment of the L-function associated to a holomorphic primitive cusp form of even weight perturbed by a new family of mollifiers. This family is a natural extens…

math.NT2016

On a mollifier of the perturbed Riemann zeta-function

Patrick Kühn, Nicolas Robles, Dirk Zeindler

The mollification $ζ (s) + ζ^{'} (s)$ put forward by Feng is computed by analytic methods coming from the techniques of the ratios conjectures of $L$ -functions. The current situation re…

math.PR2015

The order of large random permutations with cycle weights

Julia Storm, Dirk Zeindler

The order $O_{n} (σ)$ of a permutation $σ$ of $n$ objects is the smallest integer $k \geq 1$ such that the $k$ -th iterate of $σ$ gives the identity. A remarkable result about the orde…

math.PR2014

Total variation distance and the Erdős-Turán law for random permutations with polynomially growing cycle weights

Julia Storm, Dirk Zeindler

We study the model of random permutations of $n$ objects with polynomially growing cycle weights, which was recently considered by Ercolani and Ueltschi, among others. Using saddle…

math.PR2013★ 11 cited

The limit shape of random permutations with polynomially growing cycle weights

Alessandra Cipriani, Dirk Zeindler

In this work we are considering the behavior of the limit shape of Young diagrams associated to random permutations on the set ${1, \dots, n}$ under a particular class of multiplic…

math.PR2013★ 15 cited

Asymptotic statistics of cycles in surrogate-spatial permutations

Leonid V. Bogachev, Dirk Zeindler

We propose an extension of the Ewens measure on permutations by choosing the cycle weights to be asymptotically proportional to the degree of the symmetric group. This model is pri…

math.PR2013★ 7 cited

Large cycles and a functional central limit theorem for generalized weighted random permutations

Ashkan Nikeghbali, Julia Storm, Dirk Zeindler

The objects of our interest are the so-called $A$ -permutations, which are permutations whose cycle length lie in a fixed set $A$ . They have been extensively studied with respect to…

math.PR2012★ 18 cited

On the number of cycles in a random permutation

Kenneth Maples, Ashkan Nikeghbali, Dirk Zeindler

We show that the number of cycles in a random permutation chosen according to generalized Ewens measure is normally distributed and compute asymptotic estimates for the mean and va…

math.PR2011★ 8 cited

The Characteristic Polynomial of a Random Permutation Matrix at Different Points

Kim Dang, Dirk Zeindler

We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect t…

math.PR2011★ 15 cited

Random permutation matrices under the generalized Ewens measure

Christopher Hughes, Joseph Najnudel, Ashkan Nikeghbali +1

We consider a generalization of the Ewens measure for the symmetric group, calculating moments of the characteristic polynomial and similar multiplicative statistics. In addition,…

math.PR2011★ 1 cited

The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles

Ashkan Nikeghbali, Dirk Zeindler

The goal of this paper is to analyse the asymptotic behavior of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are…

math.PR2010★ 4 cited

Central limit theorem for multiplicative class functions on the symmetric group

Dirk Zeindler

Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmet…

math.PR2009★ 5 cited

On averages of randomized class functions on the symmetric groups and their asymptotics

Paul-Olivier Dehaye, Dirk Zeindler

The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices (n points). In this paper, we generalize m…

math.PR2009★ 2 cited

Permutation Matrices and the Moments of their Characteristic Polynomials

Dirk Zeindler

In this paper, we are interested in the moments of the characteristic polynomial $Z_{n} (x)$ of the $n \times n$ permutation matrices with respect to the uniform measure. We use a comb…

On the exponential sum over squarefree integers

Bilinear forms with Kloosterman fractions and applications

Exponential sums twisted by general arithmetic functions

Strange and pseudo-differentiable functions with applications to prime partitions

Partitions into semiprimes

Precise asymptotics of longest cycles in random permutations without macroscopic cycles

Long cycle of random permutations with polynomially growing cycle weights

Random permutations with logarithmic cycle weights

More than five-twelfths of the zeros of ζ are on the critical line

Random permutations without macroscopic cycles

On mean values of mollifiers and L-functions associated to primitive cusp forms

On a mollifier of the perturbed Riemann zeta-function

The order of large random permutations with cycle weights

Total variation distance and the Erdős-Turán law for random permutations with polynomially growing cycle weights

The limit shape of random permutations with polynomially growing cycle weights

Asymptotic statistics of cycles in surrogate-spatial permutations

Large cycles and a functional central limit theorem for generalized weighted random permutations

On the number of cycles in a random permutation

The Characteristic Polynomial of a Random Permutation Matrix at Different Points

Random permutation matrices under the generalized Ewens measure

The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles

Central limit theorem for multiplicative class functions on the symmetric group

On averages of randomized class functions on the symmetric groups and their asymptotics

Permutation Matrices and the Moments of their Characteristic Polynomials

More than five-twelfths of the zeros of $ζ$ are on the critical line