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Gábor Korchmáros Maria Montanucci Pietro Speziali 《Journal of Pure and Applied Algebra》2018,222(7):1810-1826
Let be the algebraic closure of a finite field of odd characteristic p. For a positive integer m prime to p, let be the transcendence degree 1 function field defined by . Let and . The extension is a non-Galois extension. Let K be the Galois closure of F with respect to H. By Stichtenoth [20], K has genus , p-rank (Hasse–Witt invariant) and a -automorphism group of order at least . In this paper we prove that this subgroup is the full -automorphism group of K; more precisely where Δ is an elementary abelian p-group of order and D has an index 2 cyclic subgroup of order . In particular, , and if K is ordinary (i.e. ) then . On the other hand, if G is a solvable subgroup of the -automorphism group of an ordinary, transcendence degree 1 function field L of genus defined over , then ; see [15]. This shows that K hits this bound up to the constant .Since has several subgroups, the fixed subfield of such a subgroup N may happen to have many automorphisms provided that the normalizer of N in is large enough. This possibility is worked out for subgroups of Δ. 相似文献
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Cristhian E. Hidber Miguel A. Xicoténcatl 《Journal of Pure and Applied Algebra》2018,222(6):1478-1488
The purpose of this article is to compute the mod 2 cohomology of , the mapping class group of the Klein bottle with q marked points. We provide a concrete construction of Eilenberg–MacLane spaces and fiber bundles , where denotes the configuration space of unordered q-tuples of distinct points in and is the classifying space of the group . Moreover, we show the mod 2 Serre spectral sequence of the bundle above collapses. 相似文献
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In this paper, we consider the following elliptic equation(0.1) where , , is differentiable in and is a given nonnegative Hölder continuous function in . The asymptotic behavior at infinity and structure of separation property of positive radial solutions with different initial data for (0.1) are discussed. Moreover, the existence and separation property of infinitely many positive solutions for Hardy equation and an equation related to Caffarelli–Kohn–Nirenberg inequality are obtained respectively, as special cases. 相似文献
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In this paper, we consider the function field analogue of the Lehmer's totient problem. Let and be the Euler's totient function of over , where is a finite field with q elements. We prove that if and only if (i) is irreducible; or (ii) , is the product of any 2 non-associate irreducibles of degree 1; or (iii) , is the product of all irreducibles of degree 1, all irreducibles of degree 1 and 2, and the product of any 3 irreducibles one each of degree 1, 2 and 3. 相似文献
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Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968
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Let be a field of q elements, where q is a power of an odd prime p. The polynomial defined by has the property that where ρ is the quadratic character on . This univariate identity was applied to prove a recent theorem of N. Katz. We formulate and prove a bivariate extension, and give an application to quadratic residuacity. 相似文献
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We establish bounds on exponential sums where , p prime, and ψ an additive character on . They extend the earlier work of Bourgain, Glibichuk, and Konyagin to fields that are not of prime order . More precisely, a non-trivial estimate is obtained provided n satisfies for all , , where is arbitrary. To cite this article: J. Bourgain, M.-C. Chang, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
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Let be an algebraically closed field of characteristic 0, and a Cohen–Macaulay graded domain with . If A is semi-standard graded (i.e., A is finitely generated as a -module), it has the h-vector, which encodes the Hilbert function of A. From now on, assume that . It is known that if A is standard graded (i.e., ), then A is level. We will show that, in the semi-standard case, if A is not level, then divides . Conversely, for any positive integers h and n, there is a non-level A with the h-vector . Moreover, such examples can be constructed as Ehrhart rings (equivalently, normal toric rings). 相似文献
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In this paper we focus our attention on the following nonlinear fractional Schrödinger equation with magnetic field where is a parameter, , , is the fractional magnetic Laplacian, and are continuous potentials and is a subcritical nonlinearity. By applying variational methods and Ljusternick–Schnirelmann theory, we prove existence and multiplicity of solutions for ε small. 相似文献
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S.E. Boutiah F. Gregorio A. Rhandi C. Tacelli 《Journal of Differential Equations》2018,264(3):2184-2204
We prove that the realization in , of the elliptic operator with domain generates a strongly continuous analytic semigroup provided that and any constants and . This generalizes the recent results in [4] and in [16]. Moreover we show that is consistent, immediately compact and ultracontractive. 相似文献