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- W4308163539 abstract "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." @default.
- W4308163539 created "2022-11-08" @default.
- W4308163539 creator A5084117128 @default.
- W4308163539 date "2022-11-02" @default.
- W4308163539 modified "2023-09-30" @default.
- W4308163539 title "Periods, Power Series, and Integrated Algebraic Numbers" @default.
- W4308163539 doi "https://doi.org/10.48550/arxiv.2211.01269" @default.
- W4308163539 hasPublicationYear "2022" @default.
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