Johannes Schoißengeier

The connection between the zeros of the ζ-function and sequences(g(p)), p prime, mod 1

In this paper we give the connection between the zeros of the ζ-function and sequences(g(p)), p prime, mod 1 ifg(x)=αxσ for α≠0, σ>0 or ifg(X) is a polynomial in ℝ.

Abschätzungen für\(\sum\limits_{n \leqslant N} {B_1 (n\alpha )} \)

AbstractEstimates for

An Explicit Formula for the L 2 -Discrepancy of ( n α )-Sequences

\sum\limits_{n \leqslant N} {B_1 (n\alpha )}

The Prime Number Theorem

. Let α∈ℝ and letB1(x)={x}−1/2. In this paper we shall give best possible estimates for

Geometry of Numbers

\sum\limits_{n = 1}^N {B_1 (n\alpha )}

Zur Metrik der Diskrepanz

. On the importance of this sum see the papers ofBehnke [2],Hardy andLittlewood [5],Hecke [6] andOstrowski [9].