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Norms in Arithmetic Progressions

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Analytic Number Theory

Part of the book series: Progress in Mathematics ((PM,volume 85))

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Abstract

The study of the distribution of various number theoretic functions in arithmetic progressions has long been a topic of concern and has in recent years received new impetus from outside sources such as exponential sums over varieties [D, B, H] and from those occurring in the theory of auto- morphic forms [D-I]. Particular examples are squarefree numbers [HB1], primes [Fo-I, B-F-I] and divisor functions [Fo, F-Il, F-I2, HB2].

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References

  1. E. Bombieri, On exponential sums in finite fields, II, Invent. Math. 47 (1978), 29–39.

    Article  MathSciNet  MATH  Google Scholar 

  2. E. Bombieri, J. Friedlander and H. Iwaniec, Primes in arithmetic progressions to large moduli III, J. Amer. Math. Soc. 2 (1989), 215–224.

    Article  MathSciNet  MATH  Google Scholar 

  3. D. A. Burgess, Estimation of character sums modulo a power of a prime, Proc. London Math. Soc. (3) 52 (1986), 215–235.

    MathSciNet  MATH  Google Scholar 

  4. P. Deligne, La conjecture de Weil I, Publ. Math. IHES 43 (1974), 273–307.

    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. J. Friedlander and H. Iwaniec, Incomplete Kloosterman sums and a divisor problem, Ann. Math. 121 (1985), 319–344; Appendix by B. J. Birch and E. Bombieri, 345–350.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Friedlander and H. Iwaniec, The divisor problem for arithmetic progressions, Acta Arith. 45 (1985), 273–277.

    MathSciNet  MATH  Google Scholar 

  8. E. Fouvry, Sur le problème des diviseurs de Titchmarsh, J. Reine Angew. Math. 357 (1985), 51–76.

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

    Google Scholar 

  11. D. R. Heath-Brown, The least square-free number in an arithmetic progression, J. Reine Angew. Math. 332 (1982), 204–220.

    Article  MathSciNet  MATH  Google Scholar 

  12. D. R. Heath-Brown, The divisor function d^{n) in arithmetic pro-gressions, Acta Arith. 47 (1986), 29–56.

    MathSciNet  MATH  Google Scholar 

  13. M. Huxley, Large values of Dirichlet polynomials, III, Acta Arith. 26 (1975), 435–444.

    MathSciNet  MATH  Google Scholar 

  14. F. Shahidi, On the Ramanujan conjecture and finiteness of poles for certain L-functions, Ann. Math. 127 (1988), 547–584.

    Article  MathSciNet  MATH  Google Scholar 

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To Paul Bateman, with friendship and respect

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© 1990 Birkhäuser Boston

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Friedlander, J.B., Iwaniec, H. (1990). Norms in Arithmetic Progressions. In: Berndt, B.C., Diamond, H.G., Halberstam, H., Hildebrand, A. (eds) Analytic Number Theory. Progress in Mathematics, vol 85. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3464-7_17

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  • DOI: https://doi.org/10.1007/978-1-4612-3464-7_17

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3481-0

  • Online ISBN: 978-1-4612-3464-7

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