4 papers
Mertens' Third Theorem for Number Fields: A New Proof, Cramér's Inequality, Oscillations, and Bias
Shehzad Hathi, Ethan S. Lee
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…
Representation of even integers as a sum of squares of primes and powers of two
Shehzad Hathi
In 1951, Linnik proved the existence of a constant such that every sufficiently large even number is the sum of two primes and at most powers of 2. Since then, this style o…
On the sum of a prime and a square-free number with divisibility conditions
Shehzad Hathi, Daniel R. Johnston
Every integer greater than two can be expressed as the sum of a prime and a square-free number. Expanding on recent work, we provide explicit and asymptotic results when divisibili…
Wolstenholme and Vandiver primes
Andrew R. Booker, Shehzad Hathi, Michael J. Mossinghoff +1
A prime is a Wolstenholme prime if mod , or, equivalently, if divides the numerator of the Bernoulli number ; a Vandiver prime is o…