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論文資訊
- 類型：已發表論文
- 日期：2021-12-28
摘要
The rich history of prime numbers includes great names such as Euclid, who first analytically studied the prime numbers and proved that there is an infinite number of them, Euler, who introduced the function ζ(s)≡∑n=1∞n-s=∏pprime11-p-s, Gauss, who estimated the rate at which prime numbers increase, and Riemann, who extended ζ(s) to the complex plane z and conjectured that all nontrivial zeros are in the R(z)=1/2 axis. The nonadditive 熵 Sq=k∑ipilnq(1/pi)(q∈R;S1=SBG≡-k∑ipilnpi, where BG stands for Boltzmann-Gibbs) on which nonextensive 統計 mechanics is based, involves the function lnqz≡z1-q-11-q(ln1z=lnz). It is already known that this function paves the way for the 湧現 of a q-generalized algebra, using q-numbers defined as ⟨x⟩q≡elnqx, which recover the number x for q=1. The q-prime numbers ar
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