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Primes in Arithmetic Progressions and Related Topics

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Analytic Number Theory and Diophantine Problems

Part of the book series: Progress in Mathematics ((PM,volume 70))

Abstract

This paper (talk) has a dual purpose. The first is to report without proof some of the results of recent collaborative work on a number of multiplicative topics. These topics are connected by a thread which we shall follow in the reverse order so that in fact the work in each section was to a greater or lesser extent motivated by the work in the subsequent sections.

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References

  1. B. J, Birch and E. Bombieri, On some exponential sums, appendix to [10], Annals of Math., 121 (1985), 345–350.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. E. Bombieri, J. B. Friedlander and H. Iwaniec, Primes in arithmetic progressions to large moduli, to appear in Acta Math

    Google Scholar 

  4. D. A. Burgess, On character sums and L-series II, Proc. London Math. Soc. (3) 13 (1963), 524–536.

    Article  MathSciNet  Google Scholar 

  5. J.-M. Deshouillers and H. Iwaniec, Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math. 70 (1982), 219–288.

    Article  MathSciNet  MATH  Google Scholar 

  6. E. Fouvry, Autour du théorème de Bombieri-Vinogradov, Acta Math. 152 (1984), 219–244.

    Article  MathSciNet  MATH  Google Scholar 

  7. E. Fouvry, Sur le problème des diviseurs de Titchmarsh, preprint (1984).

    Google Scholar 

  8. E. Fouvry, Théorème de Brun-Titchmarsh, application au théorème de Fermât, Invent. Math. 79 (1985), 383–407.

    Article  MathSciNet  MATH  Google Scholar 

  9. E. Fouvry and H. Iwaniec, Primes in arithmetic progressions, Acta Arith. 42 (1983), 197–218.

    MathSciNet  MATH  Google Scholar 

  10. J. B. Friedlander and H. Iwaniec, Incomplete Kloosterman sums and a divisor problem, Annals of Math., 121 (1985), 319–350.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. B. Friedlander and H. Iwaniec, The divisor problem for arithmetic progressions, Aeta Anith., XLV (1985), 273–277.

    MathSciNet  Google Scholar 

  12. D. R. Heath-Brown, Primes in ‘almost all’ short intervals, J. London Math. Soc. (2) 26 (1982), 385–396.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. R. Heath-Brown, Prime numbers in short intervals and a generalized Vaughan identity,Can. J. Math. 34 (1982), 1365–1377.

    Article  MathSciNet  Google Scholar 

  14. D. R. Heath-Brown and H. Iwaniec, On the difference between consecutive primes, Invent. Math. 55 (1979), 49–69.

    Article  MathSciNet  MATH  Google Scholar 

  15. C. Hooley, On exponential sums and certain of their applications, Journees Arith. 1980, Armitage, J. V. ed., Cambridge (1982), pp. 92–122.

    Google Scholar 

  16. H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307–320.

    MathSciNet  MATH  Google Scholar 

  17. H. Iwaniec, On the Brun-Titchmarsh theorem, J. Math. Soc. Japan 34 (1982), 95–123.

    Article  MathSciNet  MATH  Google Scholar 

  18. A. F. Lavrik, A functional equation for Dirichlet L-series and the problem of divisors in arithmetic progressions, Izv. Akad. Mauk SSSR Ser. Mat. 30 (1966), 433–448 (= Transl. A.M.S. (2) 82 (1969), 47–65).

    MathSciNet  MATH  Google Scholar 

  19. A. I. Vinogradov, On the density hypothesis for Dirichlet L-functions, Izv. Akad. Hank SSSR Ser. Mat. 29 (1965), 903–934; correction ibid. 30 (1966), 719–720.

    Google Scholar 

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© 1987 Birkhäuser Boston

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Friedlander, J. (1987). Primes in Arithmetic Progressions and Related Topics. In: Adolphson, A.C., Conrey, J.B., Ghosh, A., Yager, R.I. (eds) Analytic Number Theory and Diophantine Problems. Progress in Mathematics, vol 70. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4816-3_7

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  • DOI: https://doi.org/10.1007/978-1-4612-4816-3_7

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-9173-2

  • Online ISBN: 978-1-4612-4816-3

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