All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 352

Showing per page

A contribution to infinite disjoint covering systems

János Barát, Péter P. Varjú (2005)

Journal de Théorie des Nombres de Bordeaux

Let the collection of arithmetic sequences { d i n + b i : n ∈ ℤ } i ∈ I be a disjoint covering system of the integers. We prove that if d i = p k q l for some primes p , q and integers k , l ≥ 0 , then there is a j ≠ i such that d i | d j . We conjecture that the divisibility result holds for all moduli.A disjoint covering system is called saturated if the sum of the reciprocals of the moduli is equal to 1 . The above conjecture holds for saturated systems with d i such that the product of its prime factors is at most 1254 .

A Freĭman-type theorem for locally compact abelian groups

Tom Sanders (2009)

Annales de l’institut Fourier

Suppose that G is a locally compact abelian group with a Haar measure μ . The δ -ball B δ of a continuous translation invariant pseudo-metric is called d -dimensional if μ ( B 2 δ ′ ) ≤ 2 d μ ( B δ ′ ) for all δ ′ ⊂ ( 0 , δ ] . We show that if A is a compact symmetric neighborhood of the identity with μ ( n A ) ≤ n d μ ( A ) for all n ≥ d log d , then A is contained in an O ( d log 3 d ) -dimensional ball, B , of positive radius in some continuous translation invariant pseudo-metric and μ ( B ) ≤ exp ( O ( d log d ) ) μ ( A ) .

Currently displaying 41 – 60 of 352