Moment estimates for the exponential sum with higher divisor functions

Mayank Pandey

doi:10.5802/crmath.45

Number theory

Moment estimates for the exponential sum with higher divisor functions

Mayank Pandey ¹

¹ Department of Mathematics, California Institute of Technology, Pasadena, CA 91125 USA

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 419-424

Received: 2019-08-12
Revised: 2019-12-31
Accepted: 2020-03-28
Published online: 2022-05-23

DOI: 10.5802/crmath.45

Author's affiliations:

Mayank Pandey ¹

¹ Department of Mathematics, California Institute of Technology, Pasadena, CA 91125 USA

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Mayank Pandey},
     title = {Moment estimates for the exponential sum with higher divisor functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {419--424},
     year = {2022},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     doi = {10.5802/crmath.45},
     language = {en},
}

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Mayank Pandey. Moment estimates for the exponential sum with higher divisor functions. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 419-424. doi: 10.5802/crmath.45

References
Cited by

[1] daniel-fischer $L_{p}$ norm of the Dirichlet Kernel Math StackExchange. https://math.stackexchange.com/questions/2031547 (version from 11-27-2016)

[2] Henryk Iwaniec; Emmanuel Kowalski Analytic number theory, Colloquium Publications, 53, American Mathematical Society, 2004, xi+615 pages | Zbl

[3] Matti Jutila On exponential sums involving the Ramanujan function, Proc. Indian Acad. Sci., Math. Sci., Volume 97 (1987) no. 1-3, pp. 157-166 | DOI | MR

[4] Eugen Keil Moment estimates for exponential sums over $k$ -free numbers, Int. J. Number Theory, Volume 9 (2013) no. 3, pp. 607-619 | DOI | MR | Zbl

[5] Kaisa Matomäki; Maksym Radziwiłł; Terence Tao Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges (2017) (https://arxiv.org/abs/1707.01315)

[6] Robert C. Vaughan; Trevor D. Wooley On the Distribution of Generating Functions, Bull. Lond. Math. Soc., Volume 30 (1998) no. 2, pp. 113-122 | DOI | MR

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