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On a Sprindzhuk problem
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N. M. Khodzhaev
Veröffentlicht/Copyright:
1. Juni 2003
We consider estimates of the function
equal to the square-free part of the positive integer argument t . V. G. Sprindzhuk posed the following problem. Is there a constant c > 0 such that the inequality
S((n + 1) ... (n + k)) < kk
is fulfilled for an infinite number of pairs of positive integers n and k such that k < lncn? We prove that there exist positive constants c7,..., c10 such that for n ≥ c7
In the paper, we obtain several other estimates of the function S(t) and discuss some conjectures concerning S(t) and derive corollaries of those conjectures.
Published Online: 2003-06-01
Published in Print: 2003-06-01
Copyright 2003, Walter de Gruyter
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Artikel in diesem Heft
- Covering runs in binary Markov sequences
- An optimal in order method of synthesis of a search operator in the class of automaton circuits of a special form
- On the complexity of recurring sequences
- Limit theorems for the number of points of a given set covered by a random linear subspace
- On a Sprindzhuk problem
- On the activity of cell circuits realising the system of all conjunctions
Artikel in diesem Heft
- Covering runs in binary Markov sequences
- An optimal in order method of synthesis of a search operator in the class of automaton circuits of a special form
- On the complexity of recurring sequences
- Limit theorems for the number of points of a given set covered by a random linear subspace
- On a Sprindzhuk problem
- On the activity of cell circuits realising the system of all conjunctions
