Contents

# Contents

## Idea

A variant of the Bernoulli numbers introduced in Zagier 98.

## Properties

### Periodicity

The modified Bernoulli numbers $B_n$ are 12-periodic for $n$ odd 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 21, 2020 at 10:57:54. See the history of this page for a list of all contributions to it.