transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
A variant of the Bernoulli numbers introduced in Zagier 98.
The modified Bernoulli numbers are 12-periodic for odd Zagier, (A.4) (A.18).
Introduced in
Don Zagier, A modified Bernoulli number, Nieuw Archief voor Wiskunde, 16:63–72, 1998 (pdf)
Don Zagier, Hecke operators and periods of modular forms, Israel Math. Conf. Proc., 3 (1990), 321–336 (hdl:21.11116/0000-0004-3936-0)
Further discussion in
Don Zagier, Curious and Exotic Identities for Bernoulli Numbers (pdf)
Atul Dixit, Victor H. Moll, Christophe Vignat, The Zagier modification of Bernoulli numbers and a polynomial extension. Part I (arXiv:1209.4110)
The “Wheels theorem”, saying that the perturbative Chern-Simons Wilson loop observable of the unknot is, as a universal Vassiliev invariant, a series of wheel-shaped Jacobi diagrams with coefficients the modified Bernoulli numbers, is due to
following
Last revised on December 21, 2020 at 15:57:54. See the history of this page for a list of all contributions to it.