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Density of non-residues in Burgess-type intervals and applications

Abstract:
We show that for any fixed ε > 0, there are numbers δ > 0 and p0 ≥ 2 with the following property: for every prime p ≥ p0 and every integer N such that p1/(4√e) +ε ≤ N ≤ p, the sequence 1, 2, ..., N contains at least δ N quadratic non-residues modulo p. We use this result to obtain strong upper bounds on the sizes of the least quadratic non-residues in Beatty and Piatetski-Shapiro sequences. © 2008 London Mathematical Society.
Publication status:
Published

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Publisher copy:
10.1112/blms/bdm111

Authors


Garaev, MZ More by this author
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Shparlinski, IE More by this author
Journal:
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
Volume:
40
Issue:
1
Pages:
88-96
Publication date:
2008-02-05
DOI:
EISSN:
1469-2120
ISSN:
0024-6093
URN:
uuid:da560e1a-f2f9-44a2-b541-a5f65c640638
Source identifiers:
19650
Local pid:
pubs:19650
Language:
English

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