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Published in 2019 at "manuscripta mathematica"
DOI: 10.1007/s00229-018-1022-3
Abstract: This paper characterizes $${\mathrm {GL}}_n({\mathbb {F}}_q )$$GLn(Fq)-distinguished cuspidal representations of $${\mathrm {GL}}_n({\mathbb {F}}_{q^2})$$GLn(Fq2) in terms of the special values of their twisted gamma factors.
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Keywords:
factors quadratic;
quadratic extension;
gamma factors;
extension finite ... See more keywords
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Published in 2018 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-018-8024-7
Abstract: We consider the vanishing ideal of a projective space over a finite field. An explicit set of generators for this ideal has been given by Mercier and Rolland. We show that these generators form a…
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Keywords:
ideals projective;
finite fields;
footprint bound;
vanishing ideals ... See more keywords
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Published in 2018 at "Journal of Automated Reasoning"
DOI: 10.1007/s10817-018-9485-1
Abstract: We present a formalisation of the theory of finite fields, from basic axioms to their classification, both existence and uniqueness, in HOL4 using the notion of subfields. The tools developed are applied to the characterisation…
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Keywords:
fields applications;
classification finite;
finite fields;
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Published in 2018 at "Periodica Mathematica Hungarica"
DOI: 10.1007/s10998-017-0216-x
Abstract: In this paper we present an iterative construction of irreducible polynomials over finite fields based on repeated applications of transforms induced by endomorphisms of odd prime degree of ordinary elliptic curves.
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Keywords:
irreducible polynomials;
polynomials finite;
finite fields;
odd prime ... See more keywords
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Published in 2022 at "Israel Journal of Mathematics"
DOI: 10.1007/s11856-022-2290-x
Abstract: We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. Informally speaking, we show that given a fixed collection of r -colored complexity 1 arithmetic patterns over…
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Keywords:
complexity;
complexity patterns;
induced arithmetic;
finite fields ... See more keywords
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Published in 2020 at "Cryptography and Communications"
DOI: 10.1007/s12095-019-00417-y
Abstract: In this paper, we show that LCD codes are not equivalent to non-LCD codes over small finite fields. The enumeration of binary optimal LCD codes is obtained. We also get the exact value of LD(…
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Keywords:
bounds lcd;
new bounds;
codes finite;
finite fields ... See more keywords
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Published in 2018 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2017.10.029
Abstract: Abstract The cohomology of the degree-n general linear group over a finite field of characteristic p, with coefficients also in characteristic p, remains poorly understood. For example, the lowest degree previously known to contain nontrivial…
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Keywords:
nontrivial elements;
characteristic classes;
finite fields;
cohomology ... See more keywords
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Published in 2017 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2016.07.021
Abstract: Abstract Let P , Q ∈ F q [ X ] ∖ { 0 } be two coprime polynomials over the finite field F q with deg P > deg Q . We…
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Keywords:
christol theorem;
finite fields;
laurent series;
digit expansions ... See more keywords
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Published in 2017 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2017.04.005
Abstract: Abstract In this paper, we study the polynomial Gauss sums over finite fields, and present an analogue of Davenport–Hasse's theorem for the polynomial Gauss sums, which is a generalization of the previous result obtained by…
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Keywords:
sums finite;
polynomial gauss;
finite fields;
gauss sums ... See more keywords
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Published in 2019 at "Journal of Pure and Applied Algebra"
DOI: 10.1016/j.jpaa.2018.12.008
Abstract: Let $G$ be a reductive group scheme of type $A$ acting on a spherical scheme $X$. We prove that there exists a number $C$ such that the multiplicity $\dim Hom(\rho,\mathbb{C}[X(F)])$ is bounded by $C$, for…
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Keywords:
spaces finite;
bounds multiplicities;
scheme;
multiplicities spherical ... See more keywords
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Published in 2019 at "Linear Algebra and its Applications"
DOI: 10.1016/j.laa.2018.09.013
Abstract: Abstract For each non-negative integer n let A n be an n + 1 by n + 1 Toeplitz matrix over a finite field, F, and suppose for each n that A n is embedded…
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Keywords:
toeplitz matrices;
sequences toeplitz;
finite fields;
matrices finite ... See more keywords