MathDB

5

Part of 2014 Miklós Schweitzer

Problems(1)

Divergent sum of inverses

Source: Miklós Schweitzer 2014, P5

12/22/2014
Let α \alpha be a non-real algebraic integer of degree two, and let P \mathbb{P} be the set of irreducible elements of the ring \mathbb{Z}[ \alpha ] . Prove that ∑p∈P1∣p∣2=∞ \sum_{p\in \mathbb{P}}^{{}}\frac{1}{|p|^{2}}=\infty
superior algebrasuperior algebra unsolved