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These notes contain extended abstracts on the topic of explicit methods in number theory. The range of topics includes the Sato-Tate conjecure, Langlands programme, function fields, L-functions and many other topics.
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Karim Belabas, Hendrik W. Lenstra, Jr., Don B. Zagier, Explicit Methods in Number Theory. Oberwolfach Rep. 8 (2011), no. 3, pp. 1971–2044