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 sufficient conditions for pointwise convergence of Ramanujan-Fourier series of arithmetic functions of two variables. We […]

An arithmetic function f is a sieve function of range Q, if its Eratosthenes transform g = f * µ is supported in [1, Q]∩N, where g(q) ε q ε , ∀ε > 0. Here, we study the distribution of f over the so-called short arithmetic bands 1≤a≤H {n ∈ (N, 2N ] : n ≡ a (mod q)}, with H = o(N), and give […]

Hardy's theorem for the Riemann zeta-function ζ(s) says that it admits infinitely many complex zeros on the line (s) = 1 2. In this note, we give a simple proof of this statement which, to the best of our knowledge, is new.

This is a survey article covering certain important mathematical contributions of K. Ramachandra to the theory of the Riemann zeta-function and their impact on current research.

Lectures on the Riemann Zeta Function, by Henryk Iwaniec, University Lecture Series, Volume: 62, American Mathematical Society, Providence, RI, 2014, viii+119 pp., Softcover, ISBN 978-1-4704-1851.