We study the question of whether for each n there is an m 6= n with λ(m) = λ(n), where λ is Carmichael’s function. We give a “near” proof of the fact that this is the case unconditionally, and a complete conditional proof under the Extended Riemann Hypothesis. To Professor Carl Pomerance on his 65th birthday

We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics [6] for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary differential equation arising from the self-similarity condition along rarefaction waves, in a similar way as in purely normal flow. The dependence of the solution ...

Form an $n \times n$ matrix by drawing entries independently from $\{\pm1\}$ (or another fixed nontrivial finitely supported distribution in $\mathbf{Z}$) and let $\phi$ be the characteristic polynomial. Conditionally on extended Riemann hypothesis, with high probability is irreducible $\mathrm{Gal}(\phi) \geq A_n$.

Riemann-Problem and Level-Set Approaches for Homentropic Two-Fluid Flow Computations B. Koren,∗ M. R. Lewis,∗,1 E. H. van Brummelen,∗,2 and B. van Leer†,1 ∗CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands; and †University of Michigan, Department of Aerospace Engineering, Ann Arbor, Michigan 48109-2140 E-mail: [email protected], [email protected], [email protected], and br...

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...

In this article, we present characterizations of the concavity property minimal $$L^2$$ integrals degenerating to linearity in case products analytic subsets on open Riemann surfaces. As applications, obtain holding equality optimal jets extension problem from surfaces, which implies product versions parts Suita conjecture and extended conjecture, a Ohsawa for