Estimates on the number of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math>–rational solutions of variants of diagonal equations over finite fields

Pérez, Mariana; Privitelli, Melina

doi:10.1016/j.ffa.2020.101728

Cited by 2 publications

(7 citation statements)

References 32 publications

(41 reference statements)

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“…This result complements [25,Theorem 4.1] in the case that g is an univariate polynomial because the exponents d 1 , . .…”

Section: Systems Of Diagonal Equationssupporting

confidence: 79%

“…We observe that our estimate is of the same order than Weil's (see, e.g., [34]). On the other hand, this result complements [25,Theorem 4.1] because it does not require that…”

Section: Systems Of Diagonal Equationssupporting

confidence: 70%

“…These equations has been defined in [5]. There, the author provides an estimate for the case n = 1 and in [25] we improve his results in several aspects. Let V := V (f 1 , .…”

Section: Generalization: Variants Of Systems Of Diagonal Equationsmentioning

confidence: 65%

“…A concrete example of a system of the form (3.1) are the Markoff-Hurwitz systems. The Markoff-Hurwitz equations have been very well studied (see, e.g., [22], [18] and [25]) but, there are not results in the literature about this type of systems. Let t, n, d 1 , .…”

Section: Casementioning

confidence: 99%

“…[21], [24] and [34]). In [25], we obtain existence results and estimates on the number of F q -rational solutions of some variants of diagonal equations.…”

Section: Introductionmentioning

confidence: 99%

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On the number of simultaneous solutions of certain diagonal equations over finite fields

Pérez¹,

Privitelli²

2020

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In this paper we obtain explicit estimates and existence results on the number of Fq-rational solutions of certain systems defined by families of diagonal equations over finite fields. Our approach relies on the study of the geometric properties of the varieties defined by the systems involved. We apply these results to a generalization of Waring's problem and the distribution of solutions of congruences modulo a prime number.

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“…This result complements [25,Theorem 4.1] in the case that g is an univariate polynomial because the exponents d 1 , . .…”

Section: Systems Of Diagonal Equationssupporting

confidence: 79%

“…We observe that our estimate is of the same order than Weil's (see, e.g., [34]). On the other hand, this result complements [25,Theorem 4.1] because it does not require that…”

Section: Systems Of Diagonal Equationssupporting

confidence: 70%

“…These equations has been defined in [5]. There, the author provides an estimate for the case n = 1 and in [25] we improve his results in several aspects. Let V := V (f 1 , .…”

Section: Generalization: Variants Of Systems Of Diagonal Equationsmentioning

confidence: 65%

Section: Casementioning

confidence: 99%

“…[21], [24] and [34]). In [25], we obtain existence results and estimates on the number of F q -rational solutions of some variants of diagonal equations.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations