ETNC meaning in General ?

General Miscellaneous in General . 1 month ago

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What is Equivariant Tamagawa Number Conjecture mean?

In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula for pi, namely

1 − 1 3 + 1 5 − 1 7 + 1 9 − ⋯ = π 4 , {\displaystyle 1\,-\,{\frac {1}{3}}\,+\,{\frac {1}{5}}\,-\,{\frac {1}{7}}\,+\,{\frac {1}{9}}\,-\,\cdots \;=\;{\frac {\pi }{4}},\!}

by the recognition that expression on the left-hand side is also L(1) where L(s) is the Dirichlet L-function for the Gaussian field. This formula is a special case of the analytic class number formula, and in those terms reads that the Gaussian field has class number 1, and also contains four roots of unity, so accounting for the factor ¼.

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Equivariant Tamagawa Number Conjecture General
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Posted on 03 Dec 2024, this text provides information on General related to Miscellaneous in General. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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