Sur la démonstration de M. Hilbert du théorème de waring

@article{StridsbergSurLD,
  title={Sur la d{\'e}monstration de M. Hilbert du th{\'e}or{\`e}me de waring},
  author={Erik Stridsberg},
  journal={Mathematische Annalen},
  volume={72},
  pages={145-152}
}
  • E. Stridsberg
  • Published 1 June 1912
  • Mathematics
  • Mathematische Annalen
13 Citations
The First Years
On Hilbert’s solution of Waring’s problem
In 1909, Hilbert proved that for each fixed k, there is a number g with the following property: Every integer N ≥ 0 has a representation in the form N = x1k + x2k + … + xgk, where the xi are
Powers of totally positive subgroups of fields
Abstract For a formally real field F , a totally positive co-torsion subgroup S of F × and m ⩾ 1 , we prove that ( ∑ S ) m ⊆ ∑ S m . This extends a result of Becker. We prove several refinements of
On Waring’s problem (elementary methods)
The paper deals with two elementary methods for solving Waring’s problem on the representation of numbers as a sum of equal exponents in powers of natural numbers. The first method is an elementary
The Sylvester-Ramanujan System of Equations and The Complex Power Moment Problem
A classical system of algebraic equations is treated as a finite power moment problem in C and investigated on this base. Being originated from the algebraic theory of binary forms, this system is
On an identity of Hilbert
A simple proof of the polynomial identity used by Hilbert in the solution of the Waring problem is given. The proof is based on the continued fraction expansion of a certain formal hypergeometric
How Are the Prime Numbers Distributed
As I have already stressed, the various proofs of existence of infinitely many primes are not constructive and do not give an indication of how to determine the nth prime number. Equivalently, the
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References

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Prix Bolyai. avec un rapport par Henri Poincaré
ConclusionsAprès cet exposé, un long commentaire serait inutile. On voit quelle a été la variété des recherches deM. Hilbert, l'importance des problèmes auxquelles il s'est attaqué. Nous signalerons
Über die Darstellung der ganzen Zahlen als Summen vonnten Potenzen ganzer Zahlen
Die interessante Abhandlung von Herrn A. Fleck „Uber die Darstellung ganzer Zahlen als Summen von sechsten Potenzen ganzer Zahlen1)“ gibt mir Veranlassung, einige Betrachtungen mitzuteilen, die ich
Transcendenz vone und π