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math.CV2026
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…
math.CV2011
On Fabry's Gap Theorem
Jan-Christoph Schlage-Puchta
By combining Turán's proof of Fabry's gap theorem with a gap theorem of P. Szüsz we obtain a gap theorem which is more general then both these theorems.
math.CV2007
Natural boundary of Dirichlet series
Gautami Bhowmik, Jan-Christoph Schlage-Puchta
We prove some conditions on the existence of natural boundaries of Dirichlet series. We show that generically the presumed boundary is the natural one. We also give an application…