Related papers: Hasse theorem -- an elementary approach

We prove the analogue of the Heyde theorem for a-adic solenoids.

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

The main aim of this paper is to promote a certain style of doing coinductive proofs, similar to inductive proofs as commonly done by mathematicians. For this purpose, we provide a reasonably direct justification for coinductive proofs…

In this note we shall give a new proof to a quadrature formulae due to Newton.

We sketch several proofs of F\'ary--Milnor theorem.

We study Brauer-Manin obstructions to the Hasse principle and to weak approximation with special regard to effectivity questions.

We show that a simple and straightforward rational approximation to the Thomas--Fermi equation provides the slope at origin with unprecedented accuracy. We compare present approach with other available ones.

In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.

We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.

An complete exposition of Matthias Gunther's elementary proof of Nash's isometric embedding theorem.

We prove a Hasse principle for binary direct summands of the Chow motive of a smooth projective quadric Q over a number field F. Besides, we show that such summands are twists of Rost motives. In the case when F has at most one real…

The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.

We give an elementary proof of the Mazur-Tate-Teitelbaum conjecture for elliptic curves by using Kato's element.

We give a q-analogue of Gauss' divisibility theorem

We prove that the Hasse principle holds for cubic threefolds with 9 singular points over a number field.

Hanner's theorem is a classical theorem in the theory of retracts and extensors in topological spaces, which states that a local ANE is an ANE. While Hanner's original proof of the theorem is quite simple for separable spaces, it is rather…

The note contains a short elementary proof of Cayley's formula for labeled trees.

We give a short, elementary and explicit proof of the existence of Hilbert schemes of points on affine schemes. As a direct consequence we obtain the existence of the Hilbert scheme of points on any projective scheme, not necessarily of…

We survey the classical results on the prime number theorem

We prove an analogue of the prime number theorem for finite fields.