Horocycles, Asymptotic Freedom And Charge Screening In QED, Nonlinear -Model In 2 Dimensions Has A Structure Similar To The SU (N) Invariant Yang-Mills Theory In 4 Dimensions, Spinorial Geometry, Horizons And Superconformal Symmetry, Induced Gravity, Maxw

Abstract

Matteo A. Cardella brought to the notice the befuddling connection the dynamics of the horocycle flowing the modular surface $SL_{2}(\pmb{Z}) \backslash SL_{2}(\pmb{R})$ and the Riemann hypothesis. Error term for the asymptotic of the horocycle average of a modular function of rapid decay drew the attention of author who probed whether such results occur for a broader class of modular functions, including functions of polynomial growth, and of exponential growth at the cusp. Hints on their long horocycle average are derived by translating the horocycle flow dynamical problem in string theory language. Results are then proved by designing an unfolding trick involving a Theta series, related to the spectral Eisenstein series by Mellin integral transform....

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