Warren Dicks and Thomas Schick,
The spectral measure of certain elements of the complex group ring of a wreath product.
Geometriae Dedicata,  93 (2002), 121-137.    

                                               Addenda

                                             May 1, 2005


Some people object to the phrase "the Atiyah conjecture" being applied to the negation

of something Atiyah seemed to propose.  The point is well taken.  The last sentence of 

[1]   poses, as a "natural question",

 

 "A priori the L2-Betti numbers are real. Give examples where they are not integral

and even perhaps irrational."  

It is a trivial matter to give examples where they are not integral.  It could be argued that

there are examples in our article which are "perhaps irrational".

[1]  M. F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras,
      pages 43-72 in Astérisque No. 32-33, 1976.

Let us make the following observations.

    operation.jpeg

 

Christophe Pittet has drawn our attention to [2], which computes the limiting behaviour of some

functions that are almost considered in our article.

    revelle.jpeg

 

[2] David Revelle,  Heat kernel asymptotics on the lamplighter group,

     Elect. Comm. in Probab. 8 (2003), 142-154.


We say that our Lemma 6.1 is "well known, but we have not found a reference".
Sean Cleary has pointed out that the standard reference is Theorem 6.4.6 of [3].

[3]. Richard P. Stanley, Enumerative combinatorics. Vol. 2.
Cambridge Studies in Advanced Mathematics 62. CUP, Cambridge, 1999.

In the Math Review of our article the sentence 

"As an application, it is shown that the traces of projections in rational group algebras
are precisely the rational numbers in the interval [0,1]."

should really be

"For completeness, the authors show that the traces of projections in rational group

algebras are precisely the rational numbers in the interval [0,1]".  

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