000132820 001__ 132820 000132820 005__ 20240315113108.0 000132820 0247_ $$2doi$$a10.48550/arXiv.2102.10942 000132820 0248_ $$2sideral$$a137652 000132820 037__ $$aART-2021-137652 000132820 041__ $$aeng 000132820 100__ $$aAvendano, Martin 000132820 245__ $$aBivariate trinomials over finite fields 000132820 260__ $$c2021 000132820 5060_ $$aAccess copy available to the general public$$fUnrestricted 000132820 5203_ $$aWe 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. 000132820 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E22-17R$$9info:eu-repo/grantAgreement/ES/DGA/E22-20R$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2016-76868-C2-2-P$$9info:eu-repo/grantAgreement/ES/UZ/CUD2020-08 000132820 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000132820 590__ $$a0.429$$b2021 000132820 591__ $$aMATHEMATICS$$b314 / 333 = 0.943$$c2021$$dQ4$$eT3 000132820 592__ $$a0.244$$b2021 000132820 593__ $$aMathematics (miscellaneous)$$c2021$$dQ3 000132820 594__ $$a1.1$$b2021 000132820 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000132820 700__ $$0(orcid)0000-0002-6559-4722$$aMartín-Morales, Jorge$$uUniversidad de Zaragoza 000132820 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología 000132820 773__ $$g47, 3 (2021), 535-552$$pHoust. j. math.$$tHOUSTON JOURNAL OF MATHEMATICS$$x0362-1588 000132820 85641 $$uhttps://www.math.uh.edu/~hjm/Vol47-3.html$$zTexto completo de la revista 000132820 8564_ $$s344416$$uhttps://zaguan.unizar.es/record/132820/files/texto_completo.pdf$$yPostprint 000132820 8564_ $$s1139050$$uhttps://zaguan.unizar.es/record/132820/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000132820 909CO $$ooai:zaguan.unizar.es:132820$$particulos$$pdriver 000132820 951__ $$a2024-03-15-08:50:31 000132820 980__ $$aARTICLE