N. Ushiroya

collaborators

3 papers

math.NT2018

Eigenvalues of Matrices whose Elements are Ramanujan Sums or Kloosterman Sums

Noboru Ushiroya

Let $c_{q} (n)$ be the Ramanujan sums and let $S (m, n; q)$ be the Kloosterman sums. We study the eigenvalues of $q \times q$ matrices whose $(m, n)$ entry is $c_{q} (m - n)$ or $S (m, n; q)$ wh…

math.NT2016

Ramanujan-Fourier series of certain arithmetic functions of two variables

Noboru Ushiroya

We study Ramanujan-Fourier series of certain arithmetic functions of two variables. We generalize Delange's theorem to the case of arithmetic functions of two variables and give su…

math.NT2016

On some generalizations of mean value theorems for arithmetic functions of two variables

Noboru Ushiroya

Let $f : N^{2} \mapsto C$ be an arithmetic function of two variables. We study the existence of the limit: \[\displaystyle \lim_{x \to \infty} \frac{1}{x^2 (\log x)^…