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The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category

100%
Bryden J., Zvengrowski P.
Banach Center Publications
|
1998
|
tom 45
|
nr 1
25-39
EN
This note gives a complete description of the cohomology algebra of any orientable Seifert manifold with ℤ/p coefficients, for an arbitrary prime p. As an application, the existence of a degree one map from an orientable Seifert manifold onto a lens space is completely determined. A second application shows that the Lusternik-Schnirelmann category for a large class of Seifert manifolds is equal to 3, which in turn is used to verify the Ganea conjecture for these Seifert manifolds.
2
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Horizontal monotonicity of the modulus of the zeta function, L-functions, and related functions

81%
Matiyasevich Y., Saidak F., Zvengrowski P.
Acta Arithmetica
|
2014
|
tom 166
|
nr 2
189-200
EN
As usual, let s = σ + it. For any fixed value of t with |t| ≥ 8 and for σ < 0, we show that |ζ(s)| is strictly decreasing in σ, with the same result also holding for the related functions ξ of Riemann and η of Euler. The following inequality related to the monotonicity of all three functions is proved: ℜ (η'(s)/η(s)) < ℜ (ζ'(s)/ζ(s)) < ℜ (ξ'(s)/ξ(s)). It is also shown that extending the above monotonicity result for |ζ(s)|, |ξ(s)|, or |η(s)| from σ < 0 to σ < 1/2 is equivalent to the Riemann hypothesis. Similar monotonicity results will be established for all Dirichlet L-functions L(s,χ), where χ is any primitive Dirichlet character, as well as the corresponding ξ(s,χ) functions, together with the relation of this to the generalized Riemann hypothesis. Finally, these results will be interpreted in terms of the degree 1 elements of the Selberg class.
3
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Perfect transfinite numbers

50%
Zvengrowski P.
Fundamenta Mathematicae
|
1963
|
tom 52
|
nr 2
123-128
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