Class number one problem for the real quadratic fields $${{\mathbb {Q}({\sqrt{m^2+2r}})}}$$ Q ( m 2 + 2 r )

Archiv der Mathematik - We investigate the class number one problem for a parametric family of real quadratic fields of the form $$\mathbb {Q}( \sqrt{m^2+4r})$$ for certain positive integers m and r.     

On the Uniform Distribution of Certain Sequences

We investigate the uniform distribution of the sequence n as n ranges over the natural numbers and is a fixed positive real number which is not an integer. We then apply this in conjunction with the Linnik-Vaughan method to study the uniform distribution of the sequence p as p ranges over the prime numbers.     

Non-Wieferich primes in number fields and <Emphasis Type="Italic">abc</Emphasis>-conjecture

Let K/Q be an algebraic number field of class number one and let O _K be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in O _K under the assumption of the abc-conjecture for number fields.