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Cyclotomic matrices and hypergeometric functions over finite fields
Institution:1. School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, People''s Republic of China;2. Department of Mathematics, Nanjing University, Nanjing 210093, People''s Republic of China;3. School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing 211816, People''s Republic of China;1. Centre for the Mathematics of Symmetry and Computation, University of Western Australia, 35 Stirling Highway, Perth, 6009, Australia;2. Chair for Algebra and Representation Theory, RWTH Aachen University, Pontdriesch 10-16, Aachen, 52062, Germany;1. Worcester Polytechnic Institute, Dept. of Mathematical Sciences, Worcester, MA, USA;1. Departamento de Matemática, Facultad de Ciencias Económicas, UNL, Moreno 2557, 3000 Santa Fe, Argentina;2. Researcher of CONICET at FIQ, Universidad Nacional del Litoral, Santiago del Estero 2829, 3000 Santa Fe, Argentina;3. FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba, Av. Medina Allende 2144, Ciudad Universitaria, 5000 Córdoba, Argentina;4. Departamento de Matemática, Facultad de Ingeniería Química, UNL, Santiago del Estero 2829, 3000 Santa Fe, Argentina;1. Department of Mathematics, Niigata University, Niigata 950-2181, Japan;2. Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan
Abstract:With the help of hypergeometric functions over finite fields, we study some arithmetic properties of cyclotomic matrices involving characters and binary quadratic forms over finite fields. Also, we confirm some related conjectures posed by Zhi-Wei Sun.
Keywords:Determinants  Cyclotomic matrices  Hypergeometric functions over finite fields
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