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Inequalities for weighted sums of Mertens functions

  • Ramachandran Balasubramanian
  • Saminathan PonnusamyEmail author
  • Karl-Joachim Wirths
Article
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Abstract

In this article we derive some polynomial inequalities for Mertens functions.

Keywords

Möbius function Mertens function Polynomial inequality Euler’s totient function Euler-Mascheroni 

Mathematics Subject Classification

11A25 

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Notes

Acknowledgements

The authors thank the referee for his careful reading of the paper and his useful comments. The first author acknowledges the support of Indian National Science Academy through the Srinivasa Ramanujan Professorship and the Department of Science and Technology for the support through the J. C. Bose Fellowship.

References

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    Neubauer, G.: Eine empirische Untersuchung zur Mertensschen Funktion. Numer. Math. 5, 1–13 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
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    Obradović, M., Ponnusamy, S., Wirths, K.-J.: Logarithmic coefficients and a coefficient conjecture for univalent functions. Monatshefte Math. 185, 489–501 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
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    Ponnusamy, S., Wirths, K.-J.: Coefficient problems on the class $U(\lambda )$. Probl. Anal. Issues Anal. 7(25)(1), 87–103 (2018)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mathematical SciencesTaramani, ChennaiIndia
  2. 2.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia
  3. 3.Institut für Analysis und AlgebraBraunschweigGermany

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