Titlebook: Women in Numbers Europe IV; Research Directions Ramla Abdellatif,Valentijn Karemaker,Lejla Smajlov Book 2024 The Editor(s) (if applicable)

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https://doi.org/10.1007/978-3-031-52163-8arithmetic geometry; cryptography; Women in Numbers Europe; WiNE4; Eigenvarieties; Diophantine sets

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978-3-031-52165-2The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Transcendence Measure of ,For a given transcendental number . and for any polynomial ., we know that . Let . and . be the infimum of the numbers . satisfying the estimate . for all . with .. Any function greater than or equal to . is a . .. In this article, we find out a transcendence measure of . which improves the earlier results.

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Ramla Abdellatif,Valentijn Karemaker,Lejla SmajlovGathers clear and innovative chapters covering a wide range of subareas in number theory and algebraic geometry.Reports on recent progress and open problems.Features high-quality contributions by oft-

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Power Values of Power Sums: A Survey,(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.

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ORBIT