Plasmon Resonances in Nanoparticles, Their Applications to Magnetics and Relation to the Riemann Hypothesis

The review of the mathematical treatment of plasmon resonances as an eigenvalue problem for specific boundary integral equations is presented and general properties of plasmon spectrum are outlined. Promising applications of plasmon resonances to magnetics are described. Interesting relation of eigenvalue treatment of plasmon resonances to the Riemann hypothesis is discussed.