论文标题
结合Igusa对指数和单型的猜想与最小指数的半续集
Combining Igusa's conjectures on exponential sums and monodromy with semi-continuity of the minimal exponent
论文作者
论文摘要
我们将伊格萨（Igusa）的两个猜想与穆斯塔（Mustaţ）和popa的最新半持续结果结合在一起，形成了关于指数总和的新自然猜想。这些界限仅在程度和维度方面具有欺骗性的简单和一般的表述。我们提供的证据部分由有关Igusa在指数金额上的猜想进行改编的部分改编，但也包括一些新证据，例如所有多项式的新证据，最高为$ 4 $变量。我们表明，这些界限又暗示着Igusa（强）单肌猜想的后果。界限与在局部全球原理中出现的主要弧的估计值有关。
We combine two of Igusa's conjectures with recent semi-continuity results by Mustaţă and Popa to form a new, natural conjecture about bounds for exponential sums. These bounds have a deceivingly simple and general formulation in terms of degrees and dimensions only. We provide evidence consisting partly of adaptations of already known results about Igusa's conjecture on exponential sums, but also some new evidence like for all polynomials in up to $4$ variables. We show that, in turn, these bounds imply consequences for Igusa's (strong) monodromy conjecture. The bounds are related to estimates for major arcs appearing in the circle method for local-global principles.
