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

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8 papers · 1 filter

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.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.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…