Proves a general probabilistic subbasis principle yielding subsets A of k-th powers or prime powers with r_{A,h}(n) realizing any admissible regularly varying F(n), including the singular series factor, for sufficiently large h.
Pliego,On Vu’s theorem in Waring’s problem for thinner sequences
2 Pith papers cite this work. Polarity classification is still indexing.
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Piatetski-Shapiro sequences N_(c) contain thin subbases A of order h>=5 (for 1<c<2) or h>=(floor(2c)+1)(floor(2c)+2)+1 (for c>2), with r_{A,h}(n) ~ F(n) for regularly varying F satisfying the stated growth bounds.
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Waring and Waring-Goldbach subbases with prescribed representation function
Proves a general probabilistic subbasis principle yielding subsets A of k-th powers or prime powers with r_{A,h}(n) realizing any admissible regularly varying F(n), including the singular series factor, for sufficiently large h.
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Thin subbases of Piatetski-Shapiro sequences
Piatetski-Shapiro sequences N_(c) contain thin subbases A of order h>=5 (for 1<c<2) or h>=(floor(2c)+1)(floor(2c)+2)+1 (for c>2), with r_{A,h}(n) ~ F(n) for regularly varying F satisfying the stated growth bounds.