| 王赟杰.一类同余方程解数的上界估计[J].数学年刊A辑,2009,30(6):857~868 |
| 一类同余方程解数的上界估计 |
| The Estimation of an Upper Bound for the Number of Solutions of a Kind of Congruences |
| Received:February 05, 2008 Revised:May 17, 2009 |
| DOI： |
| 中文关键词: 同余方程的解数, p-adic指数赋值, 特征和 |
| 英文关键词:The number of solutions of congruences, p-adic exponential evalution, Character sums |
| 基金项目: |
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| 中文摘要: |
| 主要研究形如∏i=1r(X+mi)≡∏j=r+12r(X+mj) (mod pμ)的同余方程关于m<=(m1,…,m2r)解数估计问题,并得出当r=4,5时,该同余方程解数的上界估计. 前者可改进Dodd的结论,而后者则可应用于对另一类同余方程组解数的上界估计. |
| 英文摘要: |
| This paper investigates the estimation of the solution number about m<=(m1,…,m2r) of the
congruences such as ∏i=1r(X+mi)≡∏j=r+12r(X+mj) (mod pμ),
and gets the upper bound of the solution number of such congruence when r=4 and 5. The former result improves the Dodd's conclusion, and the latter can be used to estimate the solution number of the other kinds of congruences. |
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