Asymptotic behavior of the smallest eigenvalue of matrices associated with completely even functions (mod r)

Details Asymptotic behavior of the smallest eigenvalue of matrices associated with completely even functions (mod r) Asymptotic behavior of the smallest eigenvalue of matrices associated with completely even functions (mod r)

2008-08-29

arxiv.org/abs/0808.4118v5

International Journal of Number Theory 7 (2011), 1681-1704

Mathematics

Number Theory

23 pages. To appear in International Journal of Number Theory

Scientific paper

In this paper we present systematically analysis on the smallest eigenvalue of matrices associated with completely even functions (mod $r$). We obtain several theorems on the asymptotic behavior of the smallest eigenvalue of matrices associated with completely even functions (mod $r$). In particular, we get information on the asymptotic behavior of the smallest eigenvalue of the famous Smith matrices. Finally some examples are given to demonstrate the main results.

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