Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4583304 | Finite Fields and Their Applications | 2007 | 10 Pages |
Abstract
Terras [A. Terras, Fourier Analysis on Finite Groups and Applications, Cambridge Univ. Press, 1999] gave a conjecture on the distribution of the eigenvalues of finite upper half plane graphs. This is known as a finite analogue of Sato–Tate conjecture. There are several modified versions of them. In this paper, we show that this conjecture is not correct in its original form (i.e., Conjecture 1.1). This is shown for the calculations of the 3rd and 4th moments of the distribution of the eigenvalues. We remark that a weaker version of the conjecture (i.e., Conjecture 1.2) may still hold.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory