Annales de l’institut Fourier· 2026Q1
Exponential periods and o-minimality
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- Q1SCImago
- 2026year
Short summary
The real and imaginary parts of exponential periods are volumes of sets definable in the o-minimal structure generated by the real exponential function and sin | [0, 1].
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Key points
- Exponential periods' real and imaginary parts are volumes of sets definable in the o-minimal structure generated by exp(x) and sin(x) on [0, 1].
- This result is a weaker analogue to the characterization of ordinary periods using ℚ-semi-algebraic sets.
- A new notion of 'naive exponential period' is introduced and compared to existing definitions.
- Naive exponential periods are shown to be equivalent to periods of exponential Nori motives.
AI-generated from the title and abstract; the full text is not read.
Abstract
Let α ∈ ℂ be an exponential period. This paper shows that the real and imaginary parts of α are up to signs volumes of sets definable without parameters in the o-minimal structure generated by the real exponential function and sin | [ 0 , 1 ] . This is a weaker analogue of the precise characterisation of ordinary periods as numbers whose real and imaginary parts are up to signs volumes of ℚ -semi-algebraic sets. Furthermore, we define a notion of naive exponential period and compare it to the existing notions using cohomological methods. In particular, naive exponential periods are the same as periods of exponential Nori motives, which justifies that the definition of naive exponential periods singles out the correct set of complex numbers to be called exponential periods.
The authors' abstract, as published at the source. Annales de l’institut Fourier, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics