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modified Bernoulli number

Contents

Contents

Idea

A variant of the Bernoulli numbers introduced in Zagier 98.

Properties

Periodicity

The modified Bernoulli numbers are 12-peridic Zagier, (A.4) (A.18).

References

General

Introduced in

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)

In Chern-Simons theory

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 28, 2019 at 08:55:08. See the history of this page for a list of all contributions to it.