A subset of the integers larger than 1 is primitive if no member divides another. Erdős proved
in 1935 that the sum of $1/(a\log a) $ for $ a $ running over a primitive set $ A $ is universally …

This monograph elucidates and extends many theorems and conjectures in analytic number
theory and algebraic asymptotic analysis via the natural notions of degree and …

Rubinstein and Sarnak have shown, conditional on the Riemann hypothesis (RH) and the
linear independence hypothesis (LI) on the nonreal zeros of $\zeta (s) $, that the set of real …

Using convexity properties of reciprocals of zeta functions, especially the reciprocal of the
Riemann zeta function, we show that certain weighted Mertens sums are biased in favor of …

We provide several asymptotic expansions of the prime counting function π (x) and related
functions. We define an asymptotic continued fraction expansion of a complex-valued …

We prove that the Riemann hypothesis is equivalent to the condition for all. Here, is the
prime-counting function and is the logarithmic integral. This makes explicit a claim of Pintz …

The first result of our article is another proof of Mertens' third theorem in the number field
setting, which generalises a method of Hardy. The second result concerns the sign of the …

In this thesis, we present a few explicit results in the field of analytic number theory. The first
set of results are in the area of multiplicative number theory which deals with the behaviour …

We show that the functions $\sum_ {p\leq x}(\log p)/p-\log xE $ and $\sum_ {p\leq x} 1/p-
\log\log xB $ change sign infinitely often, and that under certain assumptions, they exhibit a …

The goal of this annotated bibliography is to record every publication on the topic of
comparative prime number theory together with a summary of its results. We use a unified …