Ueber die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen.

  title={Ueber die Erg{\"a}nzungss{\"a}tze zu den allgemeinen Reciprocit{\"a}tsgesetzen.},
  author={Ernst Eduard Kummer},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  pages={270 - 279}
  • E. Kummer
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
Jui der Abhandlung Bd. 44, pag. 93 dieses Journals, welche denselben Titel f hrt, habe ich gezeigt, dafs die auf irgend eine ideale oder wirkliche Primzahl /"(a), in der Theorie der aus λ* Wurzeln der Einheit gebildeten complexen Zahlen, sich beziehenden Indices der Zahlen l — a , λ und der complexen Einheiten durch die Zahlen der Kreistheilung in einfacher Weise bestimmt werden. Da aber diese Bestimmung nur auf die idealen Primfactoren der nichtcomplexen Primzahlen p, von der Form ρ = ΐηλ-\~1… 
Wie kann man Primzahlen erkennen
Dass die Aufgabe, die Primzahlen von den zusammengesetzten zu unterscheiden und letztere in ihre Primfactoren zu zerlegen, zu den wichtigsten und nutzlichsten der gesamten Arithmetik gehort und die
Combinatorial Potpourri: Permutations, Products, Posets, and Pfaffians
OF DISSERTATION A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the College of Arts and Sciences at the University of Kentucky By Norman
Automata and the susceptibility of the square lattice Ising model modulo powers of primes
Underline the importance of studying a new class of functions corresponding to ratios of diagonals of rational functions: they reduce to algebraic functions modulo powers of primes and they may have solutions with natural boundaries.
Literally, ”cyclotomy” signifies ”division of the circle”. The Greek geometers were taught to divide the circle into N equal parts, with ruler and compass, for N of the form 2, 23, 25, and 215.
On the support of the free Lie algebra: the Schützenberger problems
  • I. Michos
  • Mathematics
    Discret. Math. Theor. Comput. Sci.
  • 2010
It is conjecture that two words u and v of common length n, which lie in the support of the free Lie ring, are twin if and only if either u = v or n is odd and u = (v) over tilde and it is proved that it suffices to show this for a two-lettered alphabet.
Towards finite-fold Diophantine representations
The celebrated theorem established by Martin Davis, Hilary Putnam, and Julia Robinson in 1961 states that every effectively enumerable set of natural numbers has an exponential Diophantine
Parity patterns associated with lifts of Hecke groups
Let q be an odd prime, m a positive integer, and let Γm(q) be the group generated by two elements x and y subject to the relations x2m=yqm=1 and x2=yq; that is, Γm(q) is the free product of two
Almost t-complementary uniform hypergraphs
An almost t-complementary k-hypergraph is a k-uniform hypergraph with vertex set V and edge set E for which there exists a permutation $$\theta \in Sym(V)$$θ∈Sym(V) such that the sets $$E, E^\theta ,
The period-index problem for twisted topological K-theory
We introduce and solve a period-index problem for the Brauer group of a topological space. The period-index problem is to relate the order of a class in the Brauer group to the degrees of Azumaya