Application of Greenberg's conjecture in the capitulation problem
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201700467
Abstract: Let r be a positive integer. Assume Greenberg's conjecture for some totally real number fields, we show that there exists an infinite family of imaginary cyclic number fields F over the field of rational number… read more here.
Keywords: capitulation problem; application greenberg; conjecture; greenberg conjecture ... See more keywords
On Brannan’s Conjecture
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DOI: 10.1007/s00009-019-1469-9
Abstract: We prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work (Barnard et al., in Proc Am Math Soc 143(5):2117–2128,… read more here.
Keywords: brannan conjecture; conjecture;
On the Zassenhaus Conjecture for Certain Cyclic-by-Nilpotent Groups
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DOI: 10.1007/s00009-020-1479-7
Abstract: Hans Zassenhaus conjectured that every torsion unit of the integral group ring of a finite group G is conjugate within the rational group algebra to an element of the form $$\pm g$$ ± g with… read more here.
Keywords: cyclic nilpotent; conjecture certain; zassenhaus conjecture; conjecture ... See more keywords
A remark on Pólya’s conjecture at low frequencies
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DOI: 10.1007/s00013-018-1258-x
Abstract: We show that the Faber–Krahn inequality implies Pólya’s conjecture for eigenvalues $$\lambda _{k}$$λk of the Dirichlet Laplacian in $$\mathbb {R}^n$$Rn up to $$k = \lfloor b(n) \rfloor $$k=⌊b(n)⌋, where b(n) is a function with exponential… read more here.
Keywords: low frequencies; conjecture low; conjecture; remark lya ... See more keywords
Besse conjecture for compact manifolds with pinched curvature
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DOI: 10.1007/s00013-020-01463-2
Abstract: On a compact n -dimensional manifold M , it has been conjectured that a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, is… read more here.
Keywords: compact manifolds; conjecture; besse conjecture; manifolds pinched ... See more keywords
Finite graph product closure for a conjecture on the BNS-invariant of Artin groups
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DOI: 10.1007/s00013-020-01530-8
Abstract: We work with a conjecture on the BNS-invariant of Artin groups stated by Almeida and Kochloukova. We show that the class of Artin groups that satisfy this conjecture is closed under finite graph products. As… read more here.
Keywords: conjecture; artin groups; invariant artin; bns invariant ... See more keywords
A Counterexample to the “Hot Spots” Conjecture on Nested Fractals
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DOI: 10.1007/s00041-017-9524-z
Abstract: Although the “hot spots” conjecture was proved to be false on some classical domains, the problem still generates a lot of interests on identifying the domains that the conjecture hold. The question can also be… read more here.
Keywords: conjecture nested; spots conjecture; conjecture; counterexample hot ... See more keywords
A non-abelian conjecture of Tate–Shafarevich type for hyperbolic curves
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DOI: 10.1007/s00208-018-1684-x
Abstract: Let X denote a hyperbolic curve over $$\mathbb {Q}$$Q and let p denote a prime of good reduction. The third author’s approach to integral points, introduced in Kim (Invent Math 161:629–656, 2005; Publ Res Inst… read more here.
Keywords: non abelian; math soc; conjecture; abelian conjecture ... See more keywords
The strong Atiyah and Lück approximation conjectures for one-relator groups
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DOI: 10.1007/s00208-019-01926-0
Abstract: It is shown that the strong Atiyah conjecture and the Lück approximation conjecture in the space of marked groups hold for locally indicable groups. In particular, this implies that one-relator groups satisfy both conjectures. We… read more here.
Keywords: one relator; approximation; conjecture; relator groups ... See more keywords
Equivariant motivic integration and proof of the integral identity conjecture for regular functions
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DOI: 10.1007/s00208-019-01940-2
Abstract: We develop Denef–Loeser’s motivic integration to an equivariant version and use it to prove the full integral identity conjecture for regular functions. In comparison with Hartmann’s work, the equivariant Grothendieck ring defined in this article… read more here.
Keywords: conjecture regular; identity conjecture; conjecture; integral identity ... See more keywords
On the Beilinson–Bloch–Kato conjecture for Rankin–Selberg motives
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DOI: 10.1007/s00222-021-01088-4
Abstract: In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that if the central critical value… read more here.
Keywords: conjecture; rankin selberg; bloch kato; kato ... See more keywords