136,802 research outputs found
Multiplicative inverses in short intervals
We give an alternative proof of a recent result by T.D. Browning and A.
Haynes (arXiv:1204.6374v1) on multiplicative inverses in sequences of intervals
and improve this result under additional conditions on the spacing of these
intervals.Comment: 7 page
The large sieve with sparse sets of moduli
Extending a method of D. Wolke, we establish a general result on the large
sieve with sparse sets S of moduli which are in a sense well-distributed in
arithmetic progressions. We then apply our result to the case when S consists
of sqares. In this case we obtain an estimate which improves a recent result by
L. Zhao
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