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Higher order divisor problems

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Abstract

An asymptotic formula is proved for the k-fold divisor function averaged over homogeneous polynomials of degree k in \(k-1\) variables coming from incomplete norm forms.

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Notes

  1. Of course, even the upper bound \(z^{-\varepsilon }\) for any \(\varepsilon > 0\) would suffice.

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Acknowledgements

I am very grateful to Péter Maga for many useful discussions and helpful suggestions on the topic of this paper and Guohua Chen for a careful reading of the manuscript and spotting some mistakes in an earlier version.

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Authors and Affiliations

  1. Mathematisches Institut, Bunsenstr. 3-5, 37073, Göttingen, Germany

    Valentin Blomer

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  1. Valentin Blomer
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Correspondence to Valentin Blomer.

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Author supported in part by the Volkswagen Foundation, DFG grant BL 915/2, and an NSF grant while enjoying the hospitality of the Institute for Advanced Study.

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Blomer, V. Higher order divisor problems. Math. Z. 290, 937–952 (2018). https://doi.org/10.1007/s00209-018-2046-9

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  • DOI: https://doi.org/10.1007/s00209-018-2046-9

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