ON DIVISOR PROBLEMS
نویسندگان
چکیده
منابع مشابه
Compensations in small divisor problems
Several small divisor problems arising in the perturbative theory of Hamiltonian and La-grangian systems are considered. A general method that allows to prove compensations among the elementary contributions of the formal power series expansions associated to invariant surfaces is presented.
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Many interesting problems in mechanics are close to systems that can be solved exactly. In such systems it is natural to consider perturbative expansions about the known system. Frequently it is possible to compute all of the terms in the expansion recursively, which can lead to expressions involving denominators that become arbitrarily small. The convergence of these expansions is difficult to...
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Let n be a positive integer, Pd(n) denotes the product of all positive divisors of n, qd(n) denotes the product of all proper divisors of n. In this paper, we study the properties of the sequences {PdCn)} and {qd(n)}, and prove that the Makowski &. Schinzel conjecture hold for the sequences {pd(n)} and {qd(n)}.
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Here and throughout logj denotes the j-th iterated logarithm, so that log2 = log log, log3 = log log log and so on. Recall that for a real valued function f and a positive function g the symbol f = Ω(g) means that lim supx→∞ |f(x)|/g(x) > 0. We write f = Ω+(g) if lim supx→∞ f(x)/g(x) > 0, and f = Ω−(g) if lim infx→∞ f(x)/g(x) < 0. Lastly f = Ω±(g) means that f = Ω+(g) and also f = Ω−(g). Since ...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 1938
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/os-9.1.216