2019/10/11 by Luca Ghidelli, Ghidelli, Luca
Mathematics · #11B05 (Secondary) #11J17 (Primary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1910.05076
openalex publication_date 2019/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.