En Ci Nicol Leong

The summatory Mobius function M ( x ) is an important arithmetic function in number theory that contains information regarding primes and square-free numbers, and has strong links to the Riemann zeta function. Its growth rate is a difficult subject...

We investigate the sums of reciprocals to an arithmetic progression taken modulo one, that is sums of fractional parts 1/{na−y}, where a,y are real parameters. Such upper bounds are known in the literature, with many applications in number theory...

Bounds on the logarithmic derivative and the reciprocal of the Riemann zeta function are studied as they have a wide range of applications, such as computing bounds for Mertens function. In this talk, we are mainly concerned with explicit bounds...