214 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
The Lang-Trotter Conjecture on Average
For an elliptic curve over \ratq and an integer let be
the number of primes of good reduction such that the trace of the
Frobenius morphism of E/\fie_p equals . We consider the quantity
on average over certain sets of elliptic curves. More in
particular, we establish the following: If and
, then the arithmetic mean of over all
elliptic curves : with a,b\in \intz, and
is , where is some constant depending
on . This improves a result of C. David and F. Pappalardi. Moreover, we
establish an ``almost-all'' result on .Comment: 18 page
Addendum to "On the problem"
We prove that the conditions and in Theorems 3
and 4 of our recent paper "On the problem" can be omitted.Comment: 7 page
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