Note on an irrational power series

@inproceedings{Davenport1966NoteOA,
  title={Note on an irrational power series},
  author={Harold Davenport},
  year={1966}
}
Further, if a is irrational and x = reika), where k is an integer, it is easily proved that a-afii—ky) (3) fix)asr^l (0 < r < 1). 1 — r The same proof shows that if x = reid), where 6 is not congruent (mod 1) to an integral multiple of a, then/(x) =o((l — r)-1)Now suppose that in (1), and in any later sums over ra, the terms ra and — ra are taken together. Then Mordell has shown that there is another case, namely when (1/ra if ra ̂ 0, (4) On = < \ 0 if ra = 0, in which the series (1) converges… CONTINUE READING

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Power series with almost periodic coefficients

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Mordell, The series £<*»/(

L J.
  • -xein*<a), J. London Math. Soc
  • 1963
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