Titlebook: Research Directions in Number Theory; Women in Numbers V Alina Bucur,Wei Ho,Renate Scheidler Book 2024 The Editor(s) (if applicable) and Th

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Psychogenic

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Research Directions in Number Theory978-3-031-51677-1Series ISSN 2364-5733 Series E-ISSN 2364-5741

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,Generalized Ramanujan–Sato Series Arising from Modular Forms,Motivated by work of Chan, Chan, and Liu, we obtain a new general theorem that produces Ramanujan–Sato series for .. We then use it to construct explicit examples related to non-compact arithmetic triangle groups, as classified by Takeuchi. Some of our examples are new, and some reproduce existing examples.

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-Adic Measures for Reciprocals of ,-Functions of Totally Real Number Fields,We construct .-adic measures that interpolate the special values of reciprocals of .-adic .-functions of totally real number fields . at negative integers. These measures are defined by analyzing the non-constant term of partial Eisenstein series of the Hilbert modular group of ..