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Local uniformity through larger scales

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Abstract

By associating frequencies to larger scales, we provide a simpler way to derive local uniformity of multiplicative functions on average from the results of Matomäki-Radziwiłł.

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References

  1. A. Granville, K. Soundararajan. Large character sums: pretentious characters and the Polya-Vinogradov theorem. J. Amer. Math. Soc., 20 (2) (2007), 357-384.

    Article  Google Scholar 

  2. B. Green, T. Tao. The quantitative behaviour of polynomial orbits on nilmanifolds. Ann. of Math. (2), 175 (2) (2012), 465–540.

  3. K. Matomäki, M. Radziwiłł. Multiplicative functions in short intervals. Ann. of Math. (2), 183 (3) (2016), :1015-1056.

  4. K. Matomäki, M. Radziwiłł, T. Tao. Fourier uniformity of bounded multiplicative functions in short intervals on average, Invent. Math., 220 (1) (2020) 1-58.

    Article  MathSciNet  Google Scholar 

  5. K. Matomäki, M. Radziwiłł, T. Tao. An averaged form of Chowla’s conjecture. Algebra & Number Theory, 9 (9) (2015), 2167-2196.

    Article  MathSciNet  Google Scholar 

  6. K. Matomäki, M. Radziwiłł, T. Tao, J. Teräväinen, T. Ziegler. Fourier uniformity of bounded multiplicative functions in short intervals on average, arXiv:2007.15644.

  7. T. Tao. Higher Order Fourier Analysis. Graduate Texts in Mathematics. American Mathematical Society, 2014.

  8. T. Tao. Equivalence of the logarithmically averaged Chowla and Sarnak conjectures. In Number theory - Diophantine problems, uniform distribution and applications, 391-421. Springer, 2017.

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Acknowledgements

The author would like to thank Kaisa Matomäki and an anonymous referee for some helpful observations on an earlier version of this manuscript.

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Authors and Affiliations

  1. Departamento de Matemática e IMAS-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428, Buenos Aires, Argentina

    Miguel N. Walsh

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  1. Miguel N. Walsh
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Correspondence to Miguel N. Walsh.

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Walsh, M.N. Local uniformity through larger scales. Geom. Funct. Anal. 31, 981–991 (2021). https://doi.org/10.1007/s00039-021-00570-8

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  • DOI: https://doi.org/10.1007/s00039-021-00570-8

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