More Heffter Spaces via Finite Fields
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Combinatorial Designs"
DOI: 10.1002/jcd.21974
Abstract: A ( v , k ; r ) Heffter space is a resolvable ( v r , b k ) configuration whose points form a half‐set of an abelian group G and whose blocks are… read more here.
Keywords: finite fields; heffter; spaces via; via finite ... See more keywords
The bias conjecture for elliptic curves over finite fields and Hurwitz class numbers in arithmetic progressions
Sign Up to like & getrecommendations! Published in 2024 at "Mathematische Annalen"
DOI: 10.1007/s00208-024-03070-w
Abstract: In this paper, we consider a version of the bias conjecture for second moments in the setting of elliptic curves over finite fields whose trace of Frobenius lies in a fixed arithmetic progression. Contrary to… read more here.
Keywords: finite fields; curves finite; arithmetic progressions; hurwitz class ... See more keywords
Gamma factors and quadratic extension over finite fields
Sign Up to like & getrecommendations! 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. read more here.
Keywords: factors quadratic; quadratic extension; gamma factors; extension finite ... See more keywords
Vanishing Ideals of Projective Spaces over Finite Fields and a Projective Footprint Bound
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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… read more here.
Keywords: ideals projective; finite fields; footprint bound; vanishing ideals ... See more keywords
Classification of Finite Fields with Applications
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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… read more here.
Keywords: fields applications; classification finite; finite fields;
On the construction of irreducible polynomials over finite fields via odd prime degree endomorphisms of elliptic curves
Sign Up to like & getrecommendations! 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. read more here.
Keywords: irreducible polynomials; polynomials finite; finite fields; odd prime ... See more keywords
Induced arithmetic removal: complexity 1 patterns over finite fields
Sign Up to like & getrecommendations! 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… read more here.
Keywords: complexity; complexity patterns; induced arithmetic; finite fields ... See more keywords
Some new bounds on LCD codes over finite fields
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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(… read more here.
Keywords: bounds lcd; new bounds; codes finite; finite fields ... See more keywords
Modular characteristic classes for representations over finite fields
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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… read more here.
Keywords: nontrivial elements; characteristic classes; finite fields; cohomology ... See more keywords
Rational digit systems over finite fields and Christol's Theorem
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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… read more here.
Keywords: christol theorem; finite fields; laurent series; digit expansions ... See more keywords
Davenport–Hasse's theorem for polynomial Gauss sums over finite fields
Sign Up to like & getrecommendations! 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… read more here.
Keywords: sums finite; polynomial gauss; finite fields; gauss sums ... See more keywords