A note on the completeness of an exponential type sequence

作者:Fang, Jinhui*
来源:Chinese Annals of Mathematics Series B, 2011, 32(4): 527-532.
DOI:10.1007/s11401-011-0660-5

摘要

For any given coprime integers p and q greater than 1, in 1959, B. J. Birch proved that all sufficiently large integers can be expressed as a sum of pairwise distinct terms of the form p (a) q (b) . As Davenport observed, Birch's proof can be modified to show that the exponent b can be bounded in terms of p and q. In 2000, N. Hegyvari gave an effective version of this bound. The author improves this bound.

全文