The Riemann zeros as spectrum and the Riemann hypothesis

We present a spectral realization of the Riemann zeros based on the propagation of a massless Dirac fermion in a region of Rindler spacetime and under the action of delta function potentials localized on the square free integers. The corresponding Hamiltonian admits a self-adjoint extension that is tuned to the phase of the zeta function, on the critical line, in order to obtain the Riemann zeros as bound states. The model suggests a proof of the Riemann hypothesis in the limit where the potentials vanish. Finally, we propose an interferometer that may yield an experimental observation of the Riemann zeros.Comment: 33 pages, 17 figures, new abstract, simplification of several sections, changes of reference

Estimation of demand systems based on elasticities of substitution

This paper develops a model for demand-system estimations, whose coefficients are own-price Marshallian elasticities and elasticities of substitution between goods. The model satisfies the homogeneity, symmetry and, eventually, adding-up restrictions implied by consumer theory, and is primarily useful for the estimation of the demands of several goods of the same industry or group of products. The characteristics of the model are compared to other existing alternatives (logarithmic, translog, AIDS and QUAIDS demand systems). The model is finally applied to estimate the demands for several carbonated soft drinks in Argentina, and its results are presented, together with the ones obtained with the other estimation methods.Demand Systems, Elasticity of Substitution, Simultaneous Equations, Carbonated Soft Drinks

Bertrand and Price-Taking Equilibria in Markets with Product Differentiation

In this paper we show that a homogeneous-product market with multiple Bertrand equilibria becomes a market with a single Bertrand equilibrium when we introduce a small degree of product differentiation. When differentiation tends to zero, that Bertrand equilibrium converges to the unique price-taking equilibrium of the homogeneous-product market, which is in turn one of the multiple Bertrand equilibria for that market.Bertrand equilibrium, price-taking equilibrium, product differentiation