Submission date: 16 July 2020

Abstract:

Let α in ℂ be an exponential period. This is the first part of a pair of papers where we show that the real and imaginary part of α are up to signs volumes of sets definable in the o-minimal structure generated by ℚ, 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 part are up to signs volumes of ℚ-semi-algebraic sets. Furthermore, we define a notion of naive exponential periods and compare it to the existing notions using cohomological methods. This points to a relation between the theory of periods and o-minimal structures.

Mathematics Subject Classification: 11G35, 14F25, 14F40, 14P10, 03C64

Keywords and phrases:

Full text arXiv 2007.08280: pdf, ps.