## On the distribution of values of certain word maps

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- by Michael Larsen and Aner Shalev PDF
- Trans. Amer. Math. Soc.
**368**(2016), 1647-1661 Request permission

## Abstract:

We prove that, for any positive integers $m, n$, the word map $(x,y) \mapsto x^my^n$ is almost measure preserving on finite simple groups. This extends the case $m=n=2$ obtained in 2009. Along the way we obtain results of independent interest on fibers of word maps and on character values.## References

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## Additional Information

**Michael Larsen**- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 293592
- Email: mjlarsen@indiana.edu
**Aner Shalev**- Affiliation: Einstein Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel
- MR Author ID: 228986
- ORCID: 0000-0001-9428-2958
- Email: shalev@math.huji.ac.il
- Received by editor(s): August 6, 2013
- Received by editor(s) in revised form: December 26, 2013
- Published electronically: May 13, 2015
- Additional Notes: The first author was partially supported by NSF Grant DMS-1101424. The second author was partially supported by ERC Advanced Grant 247034 and the Vinik Chair in Mathematics. Both authors were partially supported by Binational Science Foundation United States-Israel Grant 2008194.
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**368**(2016), 1647-1661 - MSC (2010): Primary 20P05, 20D06
- DOI: https://doi.org/10.1090/tran/6389
- MathSciNet review: 3449221