author={COLLOQU IUM and MATHEMAT ICUM and Igor E. Shparlinski},
A study of certain Hamiltonian systems has led Y. Long to conjecture the existence of infinitely many primes which are not of the form p = 2bαnc + 1, where 1 < α < 2 is a fixed irrational number. An argument of P. Ribenboim coupled with classical results about the distribution of fractional parts of irrational multiples of primes in an arithmetic progression immediately implies that this conjecture holds in a much more precise asymptotic form. Motivated by this observation, we give an… CONTINUE READING

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 29 references

Precise iteration formulae of the Maslov-type index theory and ellipticity of closed characteristics

  • Y. Long
  • Adv. Math. 154
  • 2000
Highly Influential
5 Excerpts

The New Book of Prime Number Records

  • P. Ribenboim
  • Springer, New York
  • 1996
Highly Influential
5 Excerpts

A new estimate of the function ζ(1 + it)

  • I. M. Vinogradov
  • Izv. Akad. Nauk SSSR Ser. Mat. 22
  • 1958
Highly Influential
4 Excerpts

Exponential sums over primes in an arithmetic progression

  • A. Balog, A. Perelli
  • Proc. Amer. Math. Soc. 93
  • 1985
Highly Influential
3 Excerpts

Estimates of trigonometric sums and their applications

  • N. M. Korobov
  • Uspekhi Mat. Nauk 13
  • 1958
Highly Influential
3 Excerpts

Arithmetic functions on Beatty sequences

  • A. G. Abercrombie, W. Banks, I. E. Shparlinski
  • preprint
  • 2008
1 Excerpt