Special Elements over finite fields

• Grant number: 21/13712-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2022
• End date: July 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Herivelto Martins Borges Filho
• Grantee: José Alves Oliveira
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The main goals of this project are to understand better the conditions in which we are able to compute the number of elements in finite fields satisfying some suitable conditions and to obtain conditions that guarantee the existence of such elements. In general, the chosen problems are very interesting in the point of view of pure mathematics as well as for applications to Cryptography and Code Theory. Along the post-doc period, we will study tools used to compute the number of special elements over finite fields. One of our interests is to study sieving methods, which are well-known techniques from Number Theory that will be important in the development of our work. In particular, we will study the number/existence of primitive elements satisfying certain conditions, such as being points on curves, being in a set, or having prescribed values when evaluated in certain functions.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

OLIVEIRA, JOSE ALVES; BORGES, HERIVELTO; MARTINEZ, F. E. BROCHERO. On the number of rational points on Artin-Schreier hypersurfaces. FINITE FIELDS AND THEIR APPLICATIONS, v. 90, p. 25-pg., 2023-05-15. (22/15301-5, 21/13712-5)

OLIVEIRA, JOSE ALVES; OLIVEIRA, DANIELA; MARTINEZ, F. E. BROCHERO. The number of rational points of a class of superelliptic curves. FINITE FIELDS AND THEIR APPLICATIONS, v. 91, p. 24-pg., 2023-10-01. (21/13712-5)