ASYMPTOTIC BEHAVIOR OF THE SMALLEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (mod r)

作者：Hong Shaofang^*; Loewy Raphael

来源：International Journal of Number Theory, 2011, 7(6): 1681-1704.

DOI：10.1142/S179304211100437X

• Arithmetic progression
• completely even mod r)
• tensor product
• Dirichlet convolution
• Dirichlet's theorem
• Mertens' theorem
• Cauchy's interlacing inequalities

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.

• 出版日期2011-9
• 单位四川大学