论文标题
时期，功率系列和集成代数数字
Periods, Power Series, and Integrated Algebraic Numbers
论文作者
论文摘要
周期被定义为在理由上定义的半格式函数的积分。周期形成一个可计数的环，对不太了解。例如，通过采取抗动力来给出示例，该功率序列是在理性上的多项式环上是代数的，并以合理的数量进行评估。我们遵循这条路径并关闭这些代数功率序列，并采用迭代的抗体动力以及附近的代数和几何操作。我们获得了一个电源序列的系统，该电源序列的系数形成了可数的真实闭合场。使用O-最低限度的技术，我们能够证明每个时期属于该领域。在O最小性的情况下，我们定义指数积分的代数数，并表明Euler常数是指数式集成的代数数。因此，它们是自然数量系统延伸时环并包含重要数学常数的良好糖果。
Periods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the antiderivative of a power series which is algebraic over the polynomial ring over the rationals and evaluate it at a rational number. We follow this path and close these algebraic power series under taking iterated antiderivatives and nearby algebraic and geometric operations. We obtain a system of rings of power series whose coefficients form a countable real closed field. Using techniques from o-minimality we are able to show that every period belongs to this field. In the setting of o-minimality we define exponential integrated algebraic numbers and show that the Euler constant is an exponential integrated algebraic number. Hence they are a good candiate for a natural number system extending the period ring and containing important mathematical constants.
