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Some identities involving convolutions of Dirichlet characters and the Möbius function

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Abstract

In this paper, we present some identities involving convolutions of Dirichlet characters and the Möbius function, which are related to a well known identity of Ramanujan, Hardy and Littlewood.

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References

  1. Ahlgren S, Berndt B C, Yee A J and Zaharescu A, Integrals of Eisenstein series and derivatives of L-functions, Internat. Math. Res. Not. 32 (2002) 1723–1738

    Article  MathSciNet  MATH  Google Scholar 

  2. Andrews G E and Berndt B C, Ramanujan’s Lost Notebook, Part I, II (2005; 2009) (New York: Springer)

  3. Berndt B C, Ramanujan’s Notebooks, Parts I, II, III, and IV (1985, 1989, 1991, 1994) (New York: Springer-Verlag)

  4. Berndt B C, Ramanujan’s Notebooks, Part V (1998) (New York: Springer-Verlag)

    Book  MATH  Google Scholar 

  5. Bhaskaran R, On the versatility of Ramanujan’s ideas, Ramanujan Visiting Lectures, Technical Report 4, Madurai Kamraj University (1997) pp. 118–129

  6. Davenport H, Multiplicative number theory, 3rd ed. (2000) (New York: Springer–Verlag)

  7. Dixit A, Character analogues of Ramanujan-type integrals involving the Riemann Ξ-function, Pacific J. Math. 255 (2) (2012) 317–348

    Article  MathSciNet  MATH  Google Scholar 

  8. Dixit A, Analogues of the general theta transformation formula, Proc. Roy. Soc. Edinburgh, Sect. A 143 (2013) 371–399

    Article  MathSciNet  MATH  Google Scholar 

  9. Dixit A, Roy A and Zaharescu A, Ramanujan–Hardy–Littlewood–Riesz type phenomena for Hecke forms, J. Math. Anal. Appl. 426 (1) (2015) 594–611

    Article  MathSciNet  MATH  Google Scholar 

  10. Dixit A, Roy A and Zaharescu A, Riesz-type criteria and theta transformation analogues, J. Number Theory 160 (2016) 385–408

    Article  MathSciNet  MATH  Google Scholar 

  11. Hardy G H and Littlewood J E, Contributions to the Theory of the Riemann Zeta-Function and the Theory of the Distribution of Primes, Acta Math. 41 (1916) 119–196

    Article  MathSciNet  MATH  Google Scholar 

  12. Paris R B and Kaminski D, Asymptotics and Mellin-Barnes Integrals, Encyclopedia of Mathematics and its Applications (2001) (Cambridge: Cambridge University Press) vol. 85

  13. Ramanujan S, Notebooks (2 volumes) (1957) (Bombay: Tata Institute of Fundamental Research)

    MATH  Google Scholar 

  14. Ramanujan S, The lost notebook and other unpublished papers (1988) (New Delhi: Narosa)

    MATH  Google Scholar 

  15. Rubinstein M and Sarnak P, Chebyshev’s bias, Experiment. Math. 3 (3) (1994) 173–197

    Article  MathSciNet  MATH  Google Scholar 

  16. Titchmarsh E C, The theory of the Riemann zeta function (1986) (Oxford: Clarendon)

    MATH  Google Scholar 

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Acknowledgements

The authors would like to express their sincere gratitude to the referee for his valuable comments on an earlier version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL, 61801, USA

    Arindam Roy & Alexandru Zaharescu

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Alexandru Zaharescu

  3. Department of Mathematics, Ohio Northern University, 525 S Main Street, Ada, OH, 45810, USA

    Mohammad Zaki

Authors
  1. Arindam Roy
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  2. Alexandru Zaharescu
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  3. Mohammad Zaki
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Correspondence to Arindam Roy.

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Communicating Editor: B V Rajarama Bhat

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Roy, A., Zaharescu, A. & Zaki, M. Some identities involving convolutions of Dirichlet characters and the Möbius function. Proc Math Sci 126, 21–33 (2016). https://doi.org/10.1007/s12044-015-0256-1

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  • DOI: https://doi.org/10.1007/s12044-015-0256-1

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