Abbas Maarefparvar

In this talk, we first introduce the Brumer-Rosen-Zantema exact sequence (BRZ), a four-term sequence related to strongly ambiguous ideal classes in finite Galois extensions of number fields. Then, using BRZ, we obtain some known cohomological results...

It has been known since the 80s, thanks to Conrey and Ghosh, that the average of the square of the Riemann zeta function, summed over the extreme points of zeta up to a height $T$, is $\frac{1}{2} (e^2-5) \log T$ as $T \rightarrow \infty$. This...

The Polya group Po(K) of a Galois number field K coincides with the subgroup of the ideal class group Cl(K) of K consisting of all strongly ambiguous ideal classes. We prove that there are only finitely many imaginary abelian number fields K whose...

The Polya group P o ( K ) of a Galois number field K coincides with the subgroup of the ideal class group C l ( K ) of K consisting of all strongly ambiguous ideal classes. We prove that there are only finitely many imaginary abelian number fields K...

For a number field K, the P\'olya group of K, denoted by Po(K), is the subgroup of the ideal class group of K generated by the classes of the products of maximal ideals of K with the same norm. In this talk, after reviewing some results concerning Po...

The Polya group of a number field K is a specific subgroup of the ideal class group Cl(K) of K, generated by all classes of Ostrowski ideals of K. In this talk, I will discuss the equality Po(K)=Cl(K) in two directions. First, we will see this...

The class number one problem is one of the central subjects in algebraic number theory that turns back to the time of Gauss. This problem has led to the classical embedding problem which asks whether or not any number field K can be embedded in a...

Historically, the notion of Pólya fields dates back to some works of George Pólya and Alexander Ostrowski, in 1919, on entire functions with integer values at integers; a number field $K$ with ring of integers $\mathcal{O}_K$ is called a Pólya field...