Displaying similar documents to “Local-global principle for certain biquadratic normic bundles”

Arithmetic of 0-cycles on varieties defined over number fields

Yongqi Liang (2013)

Annales scientifiques de l'École Normale Supérieure

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Let X be a rationally connected algebraic variety, defined over a number field k . We find a relation between the arithmetic of rational points on  X and the arithmetic of zero-cycles. More precisely, we consider the following statements: (1) the Brauer-Manin obstruction is the only obstruction to weak approximation for  K -rational points on  X K for all finite extensions K / k ; (2) the Brauer-Manin obstruction is the only obstruction to weak approximation in some sense that we define for zero-cycles...

Bounds on the global offensive k-alliance number in graphs

Mustapha Chellali, Teresa W. Haynes, Bert Randerath, Lutz Volkmann (2009)

Discussiones Mathematicae Graph Theory

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Let G = (V(G),E(G)) be a graph, and let k ≥ 1 be an integer. A set S ⊆ V(G) is called a global offensive k-alliance if |N(v)∩S| ≥ |N(v)-S|+k for every v ∈ V(G)-S, where N(v) is the neighborhood of v. The global offensive k-alliance number γ ₒ k ( G ) is the minimum cardinality of a global offensive k-alliance in G. We present different bounds on γ ₒ k ( G ) in terms of order, maximum degree, independence number, chromatic number and minimum degree.

Large data local solutions for the derivative NLS equation

Ioan Bejenaru, Daniel Tataru (2008)

Journal of the European Mathematical Society

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We consider the derivative NLS equation with general quadratic nonlinearities. In [2] the first author has proved a sharp small data local well-posedness result in Sobolev spaces with a decay structure at infinity in dimension n = 2 . Here we prove a similar result for large initial data in all dimensions n ≥ 2 .

Non-local Gel'fand problem in higher dimensions

Tosiya Miyasita, Takashi Suzuki (2004)

Banach Center Publications

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The non-local Gel’fand problem, Δ v + λ e v / ∫ Ω e v d x = 0 with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.

A note on Sierpiński's problem related to triangular numbers

Maciej Ulas (2009)

Colloquium Mathematicae

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We show that the system of equations t x + t y = t p , t y + t z = t q , t x + t z = t r , where t x = x ( x + 1 ) / 2 is a triangular number, has infinitely many solutions in integers. Moreover, we show that this system has a rational three-parameter solution. Using this result we show that the system t x + t y = t p , t y + t z = t q , t x + t z = t r , t x + t y + t z = t s has infinitely many rational two-parameter solutions.

A new look at an old comparison theorem

Jaroslav Jaroš (2021)

Archivum Mathematicum

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We present an integral comparison theorem which guarantees the global existence of a solution of the generalized Riccati equation on the given interval [ a , b ) when it is known that certain majorant Riccati equation has a global solution on [ a , b ) .

Rational points on curves

Michael Stoll (2011)

Journal de Théorie des Nombres de Bordeaux

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This is an extended version of an invited lecture I gave at the Journées Arithmétiques in St. Étienne in July 2009. We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective) geometrically integral curve  C over  ℚ . The focus is on practical aspects of this problem in the case that the genus of  C is at least  2 , and therefore the set of rational points is finite.

The moduli space of totally marked degree two rational maps

Anupam Bhatnagar (2015)

Acta Arithmetica

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A rational map ϕ: ℙ¹ → ℙ¹ along with an ordered list of fixed and critical points is called a totally marked rational map. The space R a t ₂ t m of totally marked degree two rational maps can be parametrized by an affine open subset of (ℙ¹)⁵. We consider the natural action of SL₂ on R a t ₂ t m induced from the action of SL₂ on (ℙ¹)⁵ and prove that the quotient space R a t ₂ t m / S L ₂ exists as a scheme. The quotient is isomorphic to a Del Pezzo surface with the isomorphism being defined over ℤ[1/2].

Towards the Jacquet conjecture on the Local Converse Problem for p -adic GL n

Dihua Jiang, Chufeng Nien, Shaun Stevens (2015)

Journal of the European Mathematical Society

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The Local Converse Problem is to determine how the family of the local gamma factors γ ( s , π × τ , ψ ) characterizes the isomorphism class of an irreducible admissible generic representation π of GL n ( F ) , with F a non-archimedean local field, where τ runs through all irreducible supercuspidal representations of GL r ( F ) and r runs through positive integers. The Jacquet conjecture asserts that it is enough to take r = 1 , 2 , ... , n 2 . Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet...

Büchi Sequences in Local Fields and Local Rings

Jerzy Browkin (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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We prove that there exist infinite Büchi i sequences in some local rings and local fields, with the exception of the ring ℤ p of p-adic integers. In ℤ p there are only finite but arbitrarily long Büchi sequences.