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arXiv · 2308.05714

Hilbert's tenth problem for lacunary entire functions of finite order

Natalia Garcia-Fritz·Hector Pasten
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Abstract

In the context of Hilbert's tenth problem, an outstanding open case is that of complex entire functions in one variable. A negative solution is known for polynomials (by Denef) and for exponential polynomials of finite order (by Chompitaki, Garcia-Fritz, Pasten, Pheidas, and Vidaux), but no other case is known for rings of complex entire functions in one variable. We prove a negative solution to the analogue of Hilbert's tenth problem for rings of complex entire functions of finite order having lacunary power series expansion at the origin.

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Natalia Garcia-Fritz, Hector Pasten. 2023-08-10. Hilbert's tenth problem for lacunary entire functions of finite order. https://arxiv.org/abs/2308.05714

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