Distribution of prime numbers and the discrete spectrum of the Laplace operator
Copyright policy )Distribution of prime numbers and the discrete spectrum of the Laplace operator
Abstract We obtain a class of explicit formulae each of which gives an expression for the remainder term in the asymptotic equation for the Chebyshev function in terms of the spectrum of the Laplace operator on the fundamental domain of the modular group.
Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), Chebyshev psi-function, Spectral problems; spectral geometry; scattering theory on manifolds, prime numbers, spectrum of the Laplace operator, modular group
Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), Chebyshev psi-function, Spectral problems; spectral geometry; scattering theory on manifolds, prime numbers, spectrum of the Laplace operator, modular group
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