Solar energy paper index
Vector-valued smoothing for finite Sidon sets
One-line summary
A solar energy research paper on Vector-valued smoothing for finite Sidon sets.
Engineering notes
Engineering notes will be added by the Power for Solar editorial team.
Chinese explanation / 中文解读
中文解读待补充：本站会优先为光伏效率、钙钛矿太阳能电池、储能技术、太阳能热利用、BIPV、并网技术等高价值论文补充中文说明。
Original abstract
Let $F(N)$ denote the largest cardinality of a Sidon subset of $\{0, 1, \dots, N - 1\}$. We prove \[ F(N) \le N^{1/2} + 0.94601 N^{1/4} + O(1). \] This improves the recently announced coefficient $0.97633$ obtained by Carter, Georgiev, Gómez-Serrano, Hunter, O'Bryant, Tao and Wagner. It is also very close to, and numerically below, the tentatively reported value of approximately $0.947$. The argument is based on a vector-valued convolution inequality: several smoothing kernels share the task of producing a boundary majorant, while their $L^2$ energies are averaged. The analytic reduction is elementary. The final constant is supplied by a finite rational certificate, verified by a short program using exact arithmetic only.
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