Skip to main content
SpringerLink
Log in

Primes in progressions to moduli with a large power factor

  • Published:
The Ramanujan Journal Aims and scope Submit manuscript

Abstract

On average, primes are uniformly distributed in short arithmetic progressions whose moduli may be divisible by high-powers of a given integer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Barban, M.B., Linnik, Yu.V., Chudakov, N.G.: On prime numbers in an arithmetic progression with a prime-power difference. Acta Arithmetica 9, 375–390 (1964)

    MathSciNet  MATH  Google Scholar 

  2. Bombieri, E.: On the large sieve. Mathematika 12, 201–225 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  3. Elliott, P.D.T.A.: Arithmetic Functions and Integer Products. Grund. Der Math. Wiss. vol. 272, Springer-Verlag, Berlin-Heidelberg-Tokyo-New York (1985)

  4. Gallagher, P.X.: Primes in progressions to prime-power modulus of a trigonometric sum. Inventiones Math. 16, 191–201 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  5. Heath-Brown, D.R.: Zero-free regions for Dirichlet L-functions and the least prime in an arithmetic progressions. Proc. London Math. Soc. (3) 64, 265–338 (1992)

    MathSciNet  MATH  Google Scholar 

  6. Iwaniec, H.: On zeros of Dirichlet’s L-Series. Inventiones Math. 23, 97–104 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jutila, M.: On a density theorem of H. L. Montgomery for L-functions. Ann. Acad. Sci. Fenn. Ser. A.1 520, 1–13 (1972)

    Google Scholar 

  8. Montgomery, H.L.: Topics in Multiplicative Number Theory. Lecture notes in math. vol. 227. Springer-Verlag, Berlin-Heidelberg-New York (1971)

  9. Postnikov, A.G.: On the sum of the characters for a prime power modulus. Izv. Akad. Nauk. SSSR 19, 11–16 (1955)

    MathSciNet  MATH  Google Scholar 

  10. Prachar, K.: Primzahlverteilung. Grund. der math. Wiss. vol. 91, Springer-Verlag, Berlin Göttingen-Heidelberg (1957)

  11. Rosin, S.M.: On the zeros of Dirichlet L-series. Izv. Akad. Nauk. SSSR 23, 503–508 (1959)

    Google Scholar 

  12. Vinogradov, I.M.: The upper bound of the modulus of a trigonometric sum. Izv. Akad. Nauk. SSSR 14 119–214 (1950)

    Google Scholar 

  13. Vinogradov, I.M.: General theorems on the upper bound of the modulus of a trigonometric sum. Izv. Akad. Nauk. SSSR 15, 109–130 (1951)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Colorado at Boulder, Boulder, Colorado, 80309-0395

    P. D. T. A. Elliott

Authors
  1. P. D. T. A. Elliott
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

In celebration of the seventieth birthday of Richard Askey.

2000 Mathematics Subject Classification Primary—11N13

Rights and permissions

Reprints and permissions

About this article

Cite this article

Elliott, P.D.T.A. Primes in progressions to moduli with a large power factor. Ramanujan J 13, 241–251 (2007). https://doi.org/10.1007/s11139-006-0250-4

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11139-006-0250-4

Keywords

Search

Navigation