article07_2. 357KB Jun 04 2011 12:06:53 AM
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In this note we give a different and direct proof of the following result of Hall [2], which actually implies the conjecture of Sheil-Small [3].. For details about the related
Analogously to the case of square-free words, we introduce also the notions of descendant, ancestor, and closed word for minimally repetitive words, and denote by L m the set of
This new proof, however, is elementary in that it does not use the Kummer- Dedekind, nor the Kronecker Density Theorems; the proof actually shows that our sets of primes have a
In order to prove the existence theorem of local class field theory, it remains to prove the existence of cyclic, totally ramified class fields of degree p m (m ∈ N ).. We give
In view of the above remarks it seems that if one would like to produce examples of elliptic curves with large p -Selmer groups, and an irreducible representation of the Galois group
An elementary proof is given of an arithmetic for- mula, which was stated but not proved by Liouville.. An appli- cation of this formula yields a formula for the number of
While Chan and Li’s proof of Horn’s Theorem and our proof of Mirsky’s Theorem have a similar structure, there is a significant difference: The matrices whose existence is guaranteed
In this note we present a simplified proof of the zero-one law by Merkl and Zerner (2001) for directional transience of random walks in i.i.d.. Also, we indicate how to construct
