摘要翻译：
设λ是一个数值半群。假设GF(q)上存在一个具有有理位置的代数函数域，它的Weierstrass半群为λ。我们提出这样一个函数域可能有多少个有理位置的问题，我们根据λ和q的生成元导出了一个上界。我们的界是对Lewittes的界的改进，它只考虑了λ和q的多重性。在Q=2,3和4的情况下，我们对Serre的上界进行了改进。最后证明了Lewittes界对函数场塔理论的重要意义。
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英文标题：
《Bounding the number of rational places using Weierstrass semigroups》
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作者：
Olav Geil and Ryutaroh Matsumoto
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Number Theory        数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
  Let Lambda be a numerical semigroup. Assume there exists an algebraic function field over GF(q) in one variable which possesses a rational place that has Lambda as its Weierstrass semigroup. We ask the question as to how many rational places such a function field can possibly have and we derive an upper bound in terms of the generators of Lambda and q. Our bound is an improvement to a bound by Lewittes which takes into account only the multiplicity of Lambda and q. From the new bound we derive significant improvements to Serre's upper bound in the cases q=2, 3 and 4. We finally show that Lewittes' bound has important implications to the theory of towers of function fields.
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PDF链接：
https://arxiv.org/pdf/0710.4662