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Short intervals asymptotic formulae for binary problems with primes and powers, II: density 1

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Abstract

We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime square and a square, or a prime square. Such results are obtained both assuming the Riemann Hypothesis and in the unconditional case.

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Acknowledgments

This research was partially supported by the grant PRIN2010-11 Arithmetic Algebraic Geometry and Number Theory. We wish to thank the referee for his/her remarks.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121, Padova, Italy

    Alessandro Languasco

  2. Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/a, 43124, Parma, Italy

    Alessandro Zaccagnini

Authors
  1. Alessandro Languasco
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  2. Alessandro Zaccagnini
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Correspondence to Alessandro Languasco.

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Communicated by J. Schoißengeier.

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Languasco, A., Zaccagnini, A. Short intervals asymptotic formulae for binary problems with primes and powers, II: density 1. Monatsh Math 181, 419–435 (2016). https://doi.org/10.1007/s00605-015-0871-z

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  • DOI: https://doi.org/10.1007/s00605-015-0871-z

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