Titlebook: Research Directions in Number Theory; Women in Numbers IV Jennifer S. Balakrishnan,Amanda Folsom,Michelle Ma Conference proceedings 2019 Th

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Arboreal Representations for Rational Maps with Few Critical Points,Conjecture. We also exhibit a family of degree 2 rational maps and give examples of degree 3 polynomial maps whose arboreal representations have finite index in the appropriate group of tree automorphisms.

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Multiplicative Order and Frobenius Symbol for the Reductions of Number Fields,n for finitely many prime numbers .. This extends in several directions results by Moree and Sury (2009) and by Chinen and Tamura (2012), and has to be compared with the very general result of Ziegler (2006).

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Conference proceedings 2019d this volume are part of the WIN network, aimed at highlighting the research of women and gender minorities in number theory as well as increasing their participation and boosting their potential collaborations in number theory and related fields. .

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Ramanujan Graphs in Cryptography,ren–Lauter in 2006 proposed two hash functions based on the hardness of finding paths in Ramanujan graphs. One is based on Lubotzky–Phillips–Sarnak (LPS) graphs and the other one is based on Supersingular Isogeny Graphs. A 2008 paper by Petit–Lauter–Quisquater breaks the hash function based on LPS g

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