Transcriptions of Six Letters of Bernhard Riemann Preserved in the SIL
The German transcriptions of six letters of Bernhard Riemann preserved in the Smithsonian Libraries (SIL) in Washington DC are given.
math.HO↗
arXiv subjects
Wolfgang Gabcke
Publications and source records attributed to Wolfgang Gabcke.
On a Fair Copy of Riemann's 1859 Publication Created by Alfred Clebsch
We will verify that the fair copy "Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse" found in Riemann's Nachlass is not in Riemann's hand. Further, we will show that this paper was written by Alfred Clebsch and that it was used after Clebsch's death with high probability as a setting copy for chapter VII of Riemann's Collected Works published in 1876.
math.HO↗
A Parabolic Cylinder Function in the Riemann-Siegel Integral Formula
We show that the two integrals in the Riemann-Siegel integral formula can be transformed into integral representations that contain the parabolic cylinder function $U(a,z)$ as kernel function.
math.NT↗
On an Inequality Related to a Certain Fourier Cosine Series
We prove that the Fourier cosine series $\sum_{k=1}^{\infty}(-1)^{k+1}\frac{r^k\cos{kϕ}}{k+2}$ assumes its maximum value at $ϕ= 0$ for $ϕ\in [0, π)$ regardless of $r$ if $r \in (0, 1]$. This was first proved by Arias de Reyna and van de Lune. The more compact proof presented here is based on a generating function of the Chebyshev Polynomials.
math.CA↗