Results 21 to 30 of about 1,231,297 (284)
Sieving for rational points on hyperelliptic curves [PDF]
, 2001 We give a new and efficient method of sieving for rational points on hyperelliptic curves. This method is often successful in proving that a given hyperelliptic curve, suspected to have no rational points, does in fact have no rational points; we have
Siksek, Samir
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All rational one-loop Einstein-Yang-Mills amplitudes at four points
Journal of High Energy Physics, 2018 All four-point mixed gluon-graviton amplitudes in pure Einstein-Yang-Mills theory with at most one state of negative helicity are computed at one-loop order and maximal powers of the gauge coupling, using D-dimensional generalized unitarity.
Dhritiman Nandan +2 more
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Birational Quadratic Planar Maps with Generalized Complex Rational Representations
Mathematics, 2023 Complex rational maps have been used to construct birational quadratic maps based on two special syzygies of degree one. Similar to complex rational curves, rational curves over generalized complex numbers have also been constructed by substituting the ...
Xuhui Wang +4 more
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Simultaneous rational periodic points of degree-2 rational maps
Journal of Number Theory, 2023 Let $S$ be the collection of quadratic polynomial maps, and degree $2$-rational maps whose automorphism groups are isomorphic to $C_2$ defined over the rational field. Assuming standard conjectures of Poonen and Manes on the period length of a periodic point under the action of a map in $S$, we give a complete description of triples $(f_1,f_2,p)$ such ...
Burcu Barsakçı, Mohammad Sadek
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Counting algebraic numbers in short intervals with rational points
Журнал Белорусского государственного университета: Математика, информатика, 2019 In 2012 it was proved that real algebraic numbers follow a nonuniform but regular distribution, where the respective definitions go back to H. Weyl (1916) and A. Baker and W. Schmidt (1970).
Vasily I. Bernik +2 more
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Covering Rational Surfaces with Rational Parametrization Images
Mathematics, 2021 Let S be a rational projective surface given by means of a projective rational parametrization whose base locus satisfies a mild assumption. In this paper we present an algorithm that provides three rational maps f,g,h:A2⇢S⊂Pn such that the union of the ...
Jorge Caravantes +3 more
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Counting rational points on smooth cubic surfaces [PDF]
, 2016 We prove that any smooth cubic surface defined over any number field satisfies the lower bound predicted by Manin's conjecture possibly after an extension of small degree.Comment: 11 pages, minor ...
Frei, Christopher, Sofos, Efthymios
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K3 surfaces, rational curves, and rational points
Journal of Number Theory, 2010 10 pages, no figures. An explicit construction of an algebraic point lying on no smooth rational curves has been added to the end, and there have been minor revisions to the rest of the ...
Baragar, Arthur, McKinnon, David
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Frontiers in Public Health, 2022 BackgroundThe COVID-19 pandemic is a public health emergency of international concern. This study aimed to describe the cognition and social behaviors related to COVID-19 among medical college students in China and to explore the relevant factors that ...
Qiu Zhang +5 more
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Rational points of universal curves
, 2010 In this paper we prove a version of Grothendieck's section conjecture for the restriction of the universal complete curve over M_{g,n}, g > 4, to the function field k(M_{g,n}) where k is, for example, a number field.
Hain, Richard
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