Journal of University of Science and Technology of China ›› 2021, Vol. 51 ›› Issue (12): 879-888.DOI: 10.52396/JUST-2021-0077

• Research Articles • Previous Articles     Next Articles

The generating fields of two twisted Kloosterman sums

ZHANG Shenxing*   

  1. CAS Wu Wen-Tsun Key Laboratory of Mathematics, School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
  • Received:2021-03-17 Revised:2021-05-18 Online:2021-12-31 Published:2022-01-11
  • Contact: *E-mail: zsxqq@mail.ustc.edu.cn

Abstract: The generating fields of the twisted Kloosterman sums Kl (q, a, χ) and the partial Gauss sums g(q, a, χ) are studied.We require that the characteristic p is large with respect to the order d of the character χ and the trace of the coefficient a is nonzero.When p≡±1 mod d,we can characterize the generating fields of these character sums.For general p,when a lies in the prime field,we propose a combinatorial condition on (p, d) to ensure one can determine the generating fields.

Key words: Kloosterman sum, exponential sum, cyclotomic field, algebraic number

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