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<p>The monomial exponential sums have been studied extensively in the literature. Their <i>p</i>-adic valuations and algebraic degrees are unknown in general. In this paper, we first present the <i>p</i>-adic valuations of some monomial exponential sums. Then we determine their algebraic degrees, which partially answers one open problem raised by Wan.</p>

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The p-adic valuations and degrees of monomial exponential sums

  • 期刊论文

  • 发表日期：

    2025年1月29日

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  • Liping Yang,
  • Xiantao Deng

摘要

The monomial exponential sums have been studied extensively in the literature. Their p-adic valuations and algebraic degrees are unknown in general. In this paper, we first present the p-adic valuations of some monomial exponential sums. Then we determine their algebraic degrees, which partially answers one open problem raised by Wan.