Power Values of Power Sums: A Survey

Nirvana Coppola; Mar Curcó-Iranzo; Maleeha Khawaja; Vandita Patel; Özge Ülkem

doi:10.1007/978-3-031-52163-8_6

Power Values of Power Sums: A Survey

Nirvana Coppola, Mar Curcó-Iranzo, Maleeha Khawaja, Vandita Patel^*, Özge Ülkem

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

Abstract

Research on power values of power sums has gained much attention of late, partially due to the explosion of refinements in multiple advanced tools in (computational) number theory in recent years. In this survey, we present the key tools and techniques employed thus far in the (explicit) resolution of Diophantine problems, as well as an overview of existing results. We also state some open problems that naturally arise in the process.

Original language	English
Title of host publication	Women in Numbers Europe IV
Publisher	Springer
Pages	155-193
Number of pages	39
ISBN (Electronic)	978-3-031-52163-8
ISBN (Print)	978-3-031-52162-1
DOIs	https://doi.org/10.1007/978-3-031-52163-8_6
Publication status	Published - 6 Mar 2024

Publication series

Name	Association for Women in Mathematics Series
Volume	32
ISSN (Print)	2364-5733
ISSN (Electronic)	2364-5741

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Funding

N. Coppola is supported by the NWO Vidi grant No. 639.032.613, New Diophantine Directions. M. Khawaja is supported by an EPSRC studentship from the University of Sheffield (EPSRC grant no. EP/T517835/1). \u00D6. \u00DClkem is supported by T\u00DCBITAK project no. 119F405. The authors have no conflicts of interest to declare that are relevant to the content of this chapter. N. Coppola is supported by the NWO Vidi grant No. 639.032.613, New Diophantine Directions. M. Khawaja is supported by an EPSRC studentship from the University of Sheffield (EPSRC grant no. EP/T517835/1). \u00D6. \u00DClkem is supported by T\u00DCBITAK project no. 119F405. The authors have no conflicts of interest to declare that are relevant to the content of this chapter.

Funders	Funder number
Engineering and Physical Sciences Research Council
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	639.032.613
University of Sheffield	EP/T517835/1
Türkiye Bilimsel ve Teknolojik Araştırma Kurumu	119F405

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10.1007/978-3-031-52163-8_6

978-3-031-52163-8_6Final published version, 1.11 MBLicence: Taverne

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Power Values of Power Sums: A Survey

Abstract

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