A pseudoexponentiation-like structure on the algebraic numbers

Details A pseudoexponentiation-like structure on the algebraic numbers A pseudoexponentiation-like structure on the algebraic numbers

2012-02-19

arxiv.org/abs/1202.4022v1

Mathematics

Number Theory

Scientific paper

Pseudoexponential fields are exponential fields similar to complex exponentiation satisfying the Schanuel Property, which is the abstract statement of Schanuel's Conjecture, and an adapted form of existential closure. Here we show that if we remove the Schanuel Property and just care about existential closure, it is possible to create several existentially closed exponential functions on the algebraic numbers that still have similarities with complex exponentiation. The main difficulties are related to the arithmetic of algebraic numbers, and can be overcome with known results about specialisations of multiplicatively independent functions on algebraic varieties.

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