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2-Adic Stratification of Totients

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Abstract

In this paper we study the multiplicities and the asymptotic behaviour of the numbers of totients in the strata given by 2-adic valuation.

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References

  • Dickson, L.E.: A new extension of Dirichlet’s theorem on prime numbers. Messenger Math. 33, 155–161 (1904)

    Google Scholar 

  • Ford, K.: The distribution of totients. Ramanujan J. 2, 67–151 (1998)

    Article  MathSciNet  Google Scholar 

  • Ford, K.: The number of solutions of \(\phi (x)=m\). Ann. Math. 150, 1–29 (1999)

    Article  MathSciNet  Google Scholar 

  • Hardy, G.H., Ramanujan, S.: The normal number of prime factors of a number n. Q. J. Math. 48, 76–92 (1917)

    MATH  Google Scholar 

  • Maier, H., Pomerance, C.: On the number of distinct values of Euler’s \(\phi \)-function. Acta Arith. 49, 263–275 (1988)

    Article  MathSciNet  Google Scholar 

  • Pillai, S.: On some functions connected with \(\phi (n)\). Bull. Am. Math. Soc. 35, 63–70 (1929)

    MathSciNet  Google Scholar 

  • Ribenboim, P.: The new book of prime number records. Springer, Berlin (1996)

    Book  Google Scholar 

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Acknowledgements

We would like to express our appreciation to Kevin Ford for his valuable and constructive suggestions during the development of this paper. We owe a lot to the precious referee’s comments that helped us to improve the presentation of our paper.

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Authors and Affiliations

  1. Departamento de Matemática, ICEx, UFMG, Av. Antônio Carlos 6627, Belo Horizonte, MG, 30123-970, Brazil

    André Contiero

  2. Instituto de Matemática, UFAL, Av. Lourival de Melo Mota, s/n, Maceió, AL, 57072-900, Brazil

    Davi Lima

Authors
  1. André Contiero
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  2. Davi Lima
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Correspondence to André Contiero.

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Contiero, A., Lima, D. 2-Adic Stratification of Totients. Bull Braz Math Soc, New Series 53, 21–31 (2022). https://doi.org/10.1007/s00574-021-00248-7

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  • DOI: https://doi.org/10.1007/s00574-021-00248-7

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