Products with variables from low-dimensional affine spaces and shifted power identity testing in finite fields

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• 作者：Igor E. Shparlinski ^{igor.shparlinski@mq.edu.au" class="auth_mail}
• 关键词：Shifted power identity testing ; Polynomials ; Finite fields ; Linear subspaces
• 刊名：Journal of Symbolic Computation
• 出版年：August, 2014
• 年：2014
• 卷：64
• 期：Complete
• 页码：35-41
• 全文大小：219 K

文摘

Motivated by some algorithmic applications, we obtain upper bounds on the number of solutions of the equation with variables from a low-dimensional affine space in a high degree extension of a finite field. These are analogues of several recent bounds on the number of solutions of congruences of the similar form with variables in short intervals. We apply this to the recently introduced algorithmic problem of identity testing between shifted power functions in finite fields.