38 citations · 123 across the 49 of their papers we have counts for
55 papers
Newman's Tauberian theorem, the Riemann-Lebesgue Lemma, and abstract analytic number theory
Jan-Christoph Schlage-Puchta, Christoph Schwerdt
We give a generalized and effective version of Bekehermes' improvement of Newman's Tauberian theorem. To do so we prove an effective version of the Riemann-Lebesgue Lemma for funct…
On a Problem by Erdős and Mirsky on the ratio of the number of divisors of consecutive integers
Jan-Christoph Schlage-Puchta
Let be the closure of the set of all real numbers , such that there exist infinitely many integers , such that , where is the num…
The normal growth of linear groups over formal power serieses
Yiftach Barnea, Jan-Christoph Schlage-Puchta
Put $R=\F[[t_1, \ldots, t_d]])$. We estimate the number of normal subgroups of $\mathrm{SL}_2^1(\F[[t_1, \ldots, t_d]])$ for , the number of ideals in the Lie algebra $\Lie(R)…
A continuum dimensional algebra of nowhere differentiable functions
Jan-Christoph Schlage-Puchta
We construct an algebra of dimension consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhe…
Alternating state complexity of the set of primes and squarefree integers
Jan-Christoph Schlage-Puchta
We show that the set of prime numbers has exponential alternating complexity, proving a conjecture by Fijalkow. We further show that the set of squarefree integers has essentially…
Optimal version of the Picard-Lindelöf theorem
Jan-Christoph Schlage-Puchta
Consider the differential equation . We determine the weakest possible upper bound on which guarantees that this equation has for all initial values a…