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Uniform bounds in Waring’s problem over some diagonal forms

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Abstract

We investigate the existence of representations of every large positive integer as a sum of k-th powers of integers represented as certain diagonal forms. In particular, we consider a family of diagonal forms and discuss the problem of giving a uniform upper bound over the family for the number of variables needed to have such representations.

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Acknowledgements

The author’s work was supported in part by a European Research Council Advanced Grant under the European Union’s Horizon 2020 research and innovation programme via grant agreement No. 695223 during his studies at the University of Bristol. It was completed while the author was visiting Purdue University under Trevor Wooley’s supervision. The author would like to thank him for his guidance and helpful comments, and both the University of Bristol and Purdue University for their support and hospitality.

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  1. Javier Pliego

    Present address: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907-2067, USA

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  1. School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol, BS8 1UG, UK

    Javier Pliego

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  1. Javier Pliego
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Correspondence to Javier Pliego.

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Pliego, J. Uniform bounds in Waring’s problem over some diagonal forms. Math. Z. 300, 3083–3107 (2022). https://doi.org/10.1007/s00209-021-02887-4

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  • DOI: https://doi.org/10.1007/s00209-021-02887-4

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