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Conjugate variables in analytic number theory. Phase space and Lagrangian manifolds

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Abstract

For an arithmetic semigroup (G, ∂), we define entropy as a function on a naturally defined continuous semigroup Ĝ containing G. The construction is based on conditional maximization, which permits us to introduce the conjugate variables and the Lagrangian manifold corresponding to the semigroup (G, ∂).

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    V. P. Maslov

  2. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    V. P. Maslov & V. E. Nazaikinskii

  3. Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Oblast, Russia

    V. E. Nazaikinskii

Authors
  1. V. P. Maslov
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  2. V. E. Nazaikinskii
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Correspondence to V. P. Maslov.

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Maslov, V.P., Nazaikinskii, V.E. Conjugate variables in analytic number theory. Phase space and Lagrangian manifolds. Math Notes 100, 421–428 (2016). https://doi.org/10.1134/S000143461609008X

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  • DOI: https://doi.org/10.1134/S000143461609008X

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