Elementare Beweise des Primzahlsatzes mit Restglied. I.
Approximation mit algebraischen Zahlen beschränkten Grades.
Elementare Beweise des Primzahlsatzes mit Restglied. II.
Additive functions with restricted growth on the numbers of the form p+1
Functions without residue and a bilinear differential equation
On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces
On coefficient valuations of Eisenstein polynomials
Let be a prime, let . Let be the norm of under , so that is a purely ramified extension of discrete valuation rings of degree . The minimal polynomial of over is an Eisenstein polynomial; we give lower bounds for its coefficient valuations at . The function field analogue, as introduced by Carlitz and Hayes, is studied as well.
Multiplicative functions with difference tending to zero
Three two-dimensional Weyl steps in the circle problem I. The Hessian determinant
1. Summary. In a sequence of three papers we study the circle problem and its generalization involving the logarithmic mean. Most of the deeper results in this area depend on estimates of exponential sums. For the circle problem itself Chen has carried out such estimates using three two-dimensional Weyl steps with complicated techniques. We make the same Weyl steps but our approach is simpler and clearer. Crucial is a good understanding of the Hessian determinant that appears and a simple...
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