Casimir force, Casimir operators, and the Riemann hypothesis : mathematics for innovation in industry and science / editors, Gerrit van Dijk, Masato Wakayama

Frontmatter; Contents; Raising the profile of mathematics; Casimir and lessons for innovation; Mathematics in the industrial environment: Dutch perspective; The Riemann Hypothesis -- a short history; Pairing-based cryptography and its security analysis; Zeta functions and Casimir energies on infinite symmetric groups II; An algorithm for generating rational points and hash functions into elliptic curves; A Casimir force in dimer systems; Ruelle zeta function and prime geodesic theorem for hyperbolic manifolds with cusps; The dual pair (Op; q; OeSp2; 2) and Maxwell's equations

Summary

This volume contains the proceedings of the conference "Casimir Force, Casimir Operators and the Riemann Hypothesis- Mathematics for Innovation in Industry and Science" held in November 2009 in Fukuoka (Japan). The conference focused on the following topics: Casimir operators in harmonic analysis and representation theory Number theory, in particular zeta functions and cryptography Casimir force in physics and its relation with nano-science Mathematical biology Importance of mathematics for innovation in industry