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Density Modulo 1 of a Sequence Associated with a Multiplicative Function Evaluated at Polynomial Arguments

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Geometry, Algebra, Number Theory, and Their Information Technology Applications (GANITA 2016)

Abstract

The value of sums of the type

$$ \sum _{m\le n}\frac{\varphi (G(m))}{G(m)} $$

where G is a linear polynomial, a quadratic irreducible polynomial, a sequence connected with primes, etc., has been largely studied. We give here a first result concerning the distribution modulo 1 of such sequences for the case of polynomials of arbitrary degree.

         Dedicated to Professor Kumar Murty for his 60th birthday.

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References

  1. Jean-Marc Deshouillers and Mehdi Hassani, Distribution modulo \(1\) of a linear sequence associated to a multiplicative function at polynomial arguments, Science in China, Series A Mathematics 53 (2010), 2203–2206.

    Google Scholar 

  2. Jean-Marc Deshouillers and Mehdi Hassani, A note on the distribution of \(\phi (p-1)/(p-1)\), J. Australian Math. Soc.  93 (2012), 77–83.

    Google Scholar 

  3. Jean-Marc Deshouillers and Henryk Iwaniec, On the distribution modulo one of the mean values of some arithmetical functions, Uniform Distribution Theory, 3 (2008), No.1, 111–124.

    MathSciNet  MATH  Google Scholar 

  4. Jean-Marc Deshouillers and Henryk Iwaniec, On the distribution modulo one of the mean values of some arithmetical functions, Ramanujan Math. Soc. Lectures Notes 23 (2016), 19–27.

    Google Scholar 

  5. Jean-Marc Deshouillers and Florian Luca, On the distribution of some means concerning the Euler function, Functiones et Approximatio, 39, (2008), 11–20.

    MathSciNet  MATH  Google Scholar 

  6. Heini Halberstam and Hans-Egon Richert, The distribution of polynomial sequences, Mathematika, 19 (1972), 25–50.

    Article  MathSciNet  Google Scholar 

  7. Heini Halberstam and Hans-Egon Richert, Sieve Methods, Academic Press, 1974.

    Google Scholar 

  8. Godfrey Harold Hardy and Edward Maitland Wright, An introduction to the theory of numbers, Oxford University Press, 1975.

    Google Scholar 

  9. Trygve Nagell, Généralisation d’un théorème de Tchebycheff. J. Math. Pures Appl. (8) 4, (1921), 343–356.

    Google Scholar 

  10. Harold N. Shapiro, Introduction to the Theory of Numbers, Dover Publication Inc. Mineola, New York, 2008.

    Google Scholar 

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Correspondence to Jean-Marc Deshouillers .

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Deshouillers, JM., Nasiri-Zare, M. (2018). Density Modulo 1 of a Sequence Associated with a Multiplicative Function Evaluated at Polynomial Arguments. In: Akbary, A., Gun, S. (eds) Geometry, Algebra, Number Theory, and Their Information Technology Applications. GANITA 2016. Springer Proceedings in Mathematics & Statistics, vol 251. Springer, Cham. https://doi.org/10.1007/978-3-319-97379-1_7

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