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Prime in quadratic progressions on average

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Abstract

In this paper we study the distribution of primes in quadratic progressions on average. Our result improves a previous result of Baier and Zhao in some aspects.

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References

  1. Hardy, G. H., Littlewood, J. E.: Some problems of ‘Partitio numerorum’ III: on the expression of a number as sum of primes. Acta Math., 44, 1–70 (1922)

    Article  MathSciNet  Google Scholar 

  2. Baier, S., Zhao, L. Y.: Primes in quadratic progressions on average. Math. Ann., 338, 963–982 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Brünner, R., Perelli, A., Pintz, J.: The exceptional set for the sum of a prime and a square. Acta Math. Hungar., 53, 347–365 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Wang, T. Z.: On the exceptional set for the equation n = p+k 2. Acta Mathematica Sinica, English Series, 11, 156–167 (1995)

    Article  MATH  Google Scholar 

  5. Li, H. Z.: The exceptional set for the sum of a prime and a square. Acta Math. Hungar., 99, 123–141 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Vaughan, R. C.: On Goldbach’s problem. Acta Arith., 22, 21–48 (1972)

    MathSciNet  MATH  Google Scholar 

  7. Montgomery, H. L., Vaughan R. C.: The exceptional set in Goldbach’s problem. Acta Arith., 27, 353–370 (1975)

    MathSciNet  MATH  Google Scholar 

  8. Pan, C. D., Pan, C. B.: Fundamentals of Analytic Number Theory (in Chinese), Science Press, Beijing, 1991

    Google Scholar 

  9. Vaughan, R. C.: The Hardy-Littlewood Method, second edition, Cambridge University Press, Cambridge, 1997

    MATH  Google Scholar 

  10. Gallagher, P. X.: A large sieve density estimate near σ = 1. Invent. Math., 11, 329–339 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  11. Titchmarch, E. C.: The Theory of the Riemann Zeta-Function, Oxford University Press, Oxford, 1986

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shandong University, Ji’nan, 250100, P. R. China

    Guang Shi Lü & HaiWei Sun

Authors
  1. Guang Shi Lü
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  2. HaiWei Sun
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Correspondence to Guang Shi Lü.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 10701048), Shandong Province Natural Science Foundation (Grant No. ZR2009AM007), and IIFSDU

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Lü, G.S., Sun, H. Prime in quadratic progressions on average. Acta. Math. Sin.-English Ser. 27, 1187–1194 (2011). https://doi.org/10.1007/s10114-011-8059-5

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  • DOI: https://doi.org/10.1007/s10114-011-8059-5

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