The rise of secessionism in Catalonia has emerged out of the will to decide the region’s political destiny as a nation

Will Catalonia secede from Spain? Montserrat Guibernau explores why many Catalonians now hope that it might. She argues that Catalonia’s subsidization of less affluent regions, which leaves the region worse off, is a major root of discontent

The Johansen Test and the Transitivity Property

Sometimes two variables Y and Z are each cointegrated with another variable X, but Y and Z do not appear to be cointegrated with each other. This article provides a possible explanation why this might happen.cointegration

CM-points and Lattice counting on arithmetic compact Riemann surfaces

Let $X(D,1) =\Gamma(D,1) \backslash \mathbb{H}$ denote the Shimura curve of level $N=1$ arising from an indefinite quaternion algebra of fixed discriminant $D$. We study the discrete average of the error term in the hyperbolic circle problem over Heegner points of discriminant $d <0$ on $X(D,1)$ as $d \to -\infty$. We prove that if $|d|$ is sufficiently large compared to the radius $r \approx \log X$ of the circle, we can improve on the classical $O(X^{2/3})$-bound of Selberg. Our result extends the result of Petridis and Risager for the modular surface to arithmetic compact Riemann surfaces.Comment: 10 pages; Final version to appear in Journal of Number Theor