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This note proves the recurrence and rational generating function conjectured for OEIS A074003. The proof reduces the trace-and-subtrace conditions over GF(3^n) to a quadratic trace condition, evaluates the resulting character sum using quadratic Gauss sums and the Davenport-Hasse lifting formula, and derives …
We prove the conjectured trigonometric formula for the Kempner numbers (OEIS A002034). The proof uses the roots-of-unity filter to show that the cosine sum is the indicator of the divisibility condition n | m!.
We prove the conjectured trigonometric formula for the Kempner numbers (OEIS A002034). The proof uses the roots-of-unity filter to show that the cosine sum is the indicator of the divisibility condition n | m!.
This note proves the recurrence and rational generating function conjectured for OEIS A074003. The proof reduces the trace-and-subtrace conditions over GF(3^n) to a quadratic trace condition, evaluates the resulting character sum using quadratic Gauss sums and the Davenport-Hasse lifting formula, and derives …
Dian Tan, Guixu Xie, Libo Zhang, Yang Xu et autres
This repository provides the dataset associated with the manuscript entitled "Deterministic generation and distribution of genuine multipartite entanglement in macroscopic acoustic resonators." The complete datasets underlying all figures in the main text and Supplementary Materials are included in the file "Data_summary_hbar.zip". These …
Dian Tan, Guixu Xie, Libo Zhang, Yang Xu et autres
This repository provides the dataset associated with the manuscript entitled "Deterministic generation and distribution of genuine multipartite entanglement in macroscopic acoustic resonators." The complete datasets underlying all figures in the main text and Supplementary Materials are included in the file "Data_summary_hbar.zip". These …
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