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Analytic Number Theory pp 101–114Cite as

Counting Primes in Arithmetic Progressions

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Abstract

These notes represent an expanded version of a lecture delivered at the Urbana meeting of June 2014 in memory of Paul and Felice Bateman and of Heini Halberstam, and, in modified form, at the October 2014 workshop at the Royal Swedish Academy of Sciences, Stockholm, on the occasion of the presentation to Yitang Zhang of the 2014 Rolf Schock Prize in Mathematics for his ground-breaking work on bounded gaps between primes.

Keywords

  • Asymptotic Formula
  • Arithmetic Progression
  • Residue Class
  • Implied Constant
  • Sieve Method

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

To Helmut Maier on the occasion of his 60th birthday

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Notes

  1. 1.

    This co-primality restriction is assumed throughout, though not always explicitly mentioned.

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Acknowledgements

The author’s research is partially supported by a University Professor Grant from the University of Toronto and by the Natural Sciences and Engineering Research Council of Canada through Research Grant A5123.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, ON, Canada, M5S 2E4

    John B. Friedlander

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  1. John B. Friedlander
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Correspondence to John B. Friedlander .

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Editors and Affiliations

  1. Department of Mathematics, Dartmouth College, Hanover, New Hampshire, USA

    Carl Pomerance

  2. Department of Mathematics, ETH-Zürich, Zürich, Switzerland

    Michael Th. Rassias

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Friedlander, J.B. (2015). Counting Primes in Arithmetic Progressions. In: Pomerance, C., Rassias, M. (eds) Analytic Number Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-22240-0_7

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