ETNC meaning in General ?

Answer: 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.

reference

Full Form	Category
Equivariant Tamagawa Number Conjecture	General
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