8 citations · 13 across the 5 of their papers we have counts for
5 papers
Optimal stretching for lattice points under convex curves
Sinan Ariturk, Richard S. Laugesen
Suppose we count the positive integer lattice points beneath a convex decreasing curve in the first quadrant having equal intercepts. Then stretch in the coordinate directions so a…
Eigenvalue estimates on quantum graphs
Sinan Ariturk
On a finite connected metric graph, we establish upper bounds for the eigenvalues of the Laplacian. These bounds depend on the length, the Betti number, and the number of pendant v…
Eigenvalue maximization for surfaces of revolution with prescribed boundary
Sinan Ariturk
Fix two parallel circles in centered about a common axis. Among surfaces of revolution immersed in whose boundary is given by these circles, there is…
A disc maximizes Laplace eigenvalues among isoperimetric surfaces of revolution
Sinan Ariturk
The Dirichlet eigenvalues of the Laplace-Beltrami operator are larger on a flat disc than on any other surface of revoltuion immersed in Euclidean space with the same boundary.
Neumann spectral cluster estimates outside convex obstacles
Sinan Ariturk
This paper concerns spectral clusters of the Neumann Laplacian on compact Riemannian manifolds with strictly geodesically concave boundary. We prove an inequality which controls th…