Arithmetic properties of cubic and biquadratic theta series
Number Theory
2019-10-14 v1
Abstract
A cubic (resp. biquadratic) theta series is a power series whose n-th coefficient is equal to 1 if n is a perfect cube (resp. fourth power) and zero otherwise. We improve on a result of Bradshaw by showing that such series is not a cubic (resp. biquadratic) algebraic number when evaluated at reciprocals of integers. The proof relies on a "nested gaps technique" for linear independence and on recent results by the author on Waring's problem for cubes and biquadrates.
Keywords
Cite
@article{arxiv.1910.05076,
title = {Arithmetic properties of cubic and biquadratic theta series},
author = {Luca Ghidelli},
journal= {arXiv preprint arXiv:1910.05076},
year = {2019}
}