Handbook of Number Theory II

Sándor, József; Crstici, B.

doi:10.1007/1-4020-2547-5

Cited by 190 publications

(168 citation statements)

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“…Let be a prime number, observe that α ∈ B =⇒ α ≤ 2 (11) Indeed, by the equality √ ≤ ( ) which holds for > 6, cf. [21], we get that if ∈ B, then √ ≤ ( ) ≤ , thus ≤ 2 . We verify that for α = ≤ 6 the implication (11) also holds.…”

Section: Continuous and Smooth Categories: J[ ] Equal To Onementioning

confidence: 91%

Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers

Graff

Kaczkowska

2012

Open Mathematics

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Let be a smooth self-map of -dimensional, ≥ 4, smooth closed connected and simply-connected manifold, a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[ ] which is equal to the minimal number of periodic points with the periods less or equal to in the smooth homotopy class of .In this paper the invariant J[ ] is computed for self-maps of 4-manifold M with dim H 2 (M; Q) ≤ 4 and estimated for other types of manifolds. We also use J[ ] to compare minimization of the number of periodic points in smooth and in continuous categories. MSC:37C25, 55M20, 37C05

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Section: Continuous and Smooth Categories: J[ ] Equal To Onementioning

confidence: 91%

Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers

Graff

Kaczkowska

2012

Open Mathematics

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“…But, the number of divisors of n is greater than the number of unitary divisors of n, so Sitaramachandrarao and Surynarayana pointed out in [8] the following estimate of s*(n):…”

Section: Conducting Simple Calculations and Accounting Formentioning

confidence: 99%

A refinement of Sándor-Tóth's inequality

2012

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“…Число гольдбаховых пар таково, что существует постоян-ная c 1 , для которой R(q) < c 1 · ψ(q)/q (см. работы [13] или [14]). Применяя метод, использованный в работе [3] при вычислении чисел-чемпионов для ψ(q)/q, получим, что c 1 ≡ ζ(2).…”

Section: о гольдбаховых парах в примориальных размерностях и гипотезеunclassified