A useful tool to identify recessions in the euro area

This paper investigates the identification and dating of the European business cycle, using different methods. We concentrate on methods and statistical series that provide timely and accurate information about the contemporaneous state of the economy in order to provide the reader with a useful tool that allows him or her to analyze current business conditions and make predictions about the future state of the economy. In this spirit, we find that the European Commission industrial confidence indicator (ICI) is useful in providing that information.business cycle, confidence indicators, markov switching, turning points, recession, tool to identify recessions in the euro area, Bengoechea, P�rez Quir�s,

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Jaume CASALS, L'experiment d'Aristòtil

Galois action on special theta values

For a primitive Dirichlet character χ of conductor N set θχ(τ) = ∑n ∈ℤ n∈ χ(n) eπin2τ/N (where ∈ = 0 for even χ, ∈ = 1 for odd χ) the associated theta series. Its value at its point of symmetry under the modular transformation τ(image found)−1/τ is related by θχ(i) = W(χ)θ(image found) (i) to the root number of the L-series of χ and hence can be used to calculate the latter quickly if it does not vanish. Using Shimura’s reciprocity law, we calculate the Galois action on these special values of theta functions with odd N normalised by the Dedekind eta function. As a consequence, we prove some experimental results of Cohen and Zagier and we deduce a partial result on the non-vanishing of these special theta values with prime N