Redheffer

Return the $n \times n$ matrix with entry $(i,j)$ (counting from zero) set to

$$\begin{split}\begin{array}{ll} 1, & j = 0, \text{ or } (j+1) \bmod (i+1) = 0, \\ 0, & \text{otherwise}. \end{array}\end{split}$$

The determinants of such matrices are connected to the Riemann hypothesis, which holds if and only if

$$\text{det}(R) = O(n^{1/2+\epsilon})$$

for every $\epsilon > 0$.

C++ API

void Redheffer(Matrix<T> &R, Int n)

void Redheffer(AbstractDistMatrix<T> &R, Int n)

C API

ElError ElRedheffer_i(ElMatrix_i R, ElInt n)

ElError ElRedheffer_s(ElMatrix_s R, ElInt n)

ElError ElRedheffer_d(ElMatrix_d R, ElInt n)

ElError ElRedheffer_c(ElMatrix_c R, ElInt n)

ElError ElRedheffer_z(ElMatrix_z R, ElInt n)

ElError ElRedhefferDist_i(ElDistMatrix_i R, ElInt n)

ElError ElRedhefferDist_s(ElDistMatrix_s R, ElInt n)

ElError ElRedhefferDist_d(ElDistMatrix_d R, ElInt n)

ElError ElRedhefferDist_c(ElDistMatrix_c R, ElInt n)

ElError ElRedhefferDist_z(ElDistMatrix_z R, ElInt n)

Python API

Redheffer(R, n)