132820 20240315113108.0 doi 10.48550/arXiv.2102.10942 sideral 137652 ART-2021-137652 eng Avendano, Martin Bivariate trinomials over finite fields 2021 We study the number of points in the family of plane curves defined by a trinomial with fixed exponents and varying coefficients over finite fields. We prove that each of these curves has an almost predictable number of points, given by a closed formula that depends on the coefficients, the exponents, and the field, with a small error term for which we provide an upper bound in terms of an analog of the genus and the size of the field. We obtain these upper bounds from some linear and quadratic identities that the error terms satisfy. These identities are, in some cases, strong enough to determine the error terms completely. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/DGA/E22-17R info:eu-repo/grantAgreement/ES/DGA/E22-20R info:eu-repo/grantAgreement/ES/MINECO/MTM2016-76868-C2-2-P info:eu-repo/grantAgreement/ES/UZ/CUD2020-08 info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 0.429 2021 MATHEMATICS 314 / 333 = 0.943 2021 Q4 T3 0.244 2021 Mathematics (miscellaneous) 2021 Q3 1.1 2021 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Martín-Morales, Jorge Universidad de Zaragoza (orcid)0000-0002-6559-4722 2006 440 Universidad de Zaragoza Dpto. Matemáticas Área Geometría y Topología 47, 3 (2021), 535-552 Houst. j. math. HOUSTON JOURNAL OF MATHEMATICS 0362-1588 https://www.math.uh.edu/~hjm/Vol47-3.html Texto completo de la revista 344416 http://zaguan.unizar.es/record/132820/files/texto_completo.pdf Postprint 1139050 http://zaguan.unizar.es/record/132820/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:132820 articulos driver 2024-03-15-08:50:31 ARTICLE