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Let Fp,t(n) denote the number of the coefficients of (x1+x2+⋯+xt)j, 0 ≤j≤n−1, which are not divisible by the prime p. Define Gp,t(n) = Fp,t/nθ and β(p,t) = lim infFp,t)(n)/nθ, where $$ \theta = \left( {\log \left( {_t^{p + t - 1} } \right)} \right)/\left( {\log \;p} \right). $$ In this paper, we mainly prove that Gp,t can be extended to a continuous function on ℝ+,...
Abstract Let Fp,t(n) denote the number of the coefficients of (x1+1x2+...+xt)j, 0 jn 1, which are not divisible by the prime p. Define Gp,t(n) = Fp,t/n and (p,t) = lim infFp,t)(n)/n, where = (log[MATHEMATICAL FORMULA])/(log p). In this paper, we mainly prove that Gp,t can be extended to a continuous function on +, and the function Gp,t is nowhere monotonic. Both the set of differential points of the...
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