Circle problem and the spectrum of the Laplace operator on closed 2-manifolds
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Publication:5220257
DOI10.1070/RM9911zbMath1441.11260OpenAlexW2982426003MaRDI QIDQ5220257
Publication date: 11 March 2020
Published in: Russian Mathematical Surveys (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1070/rm9911
Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Lattice points in specified regions (11P21) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)
Related Items
Spectrum of the Laplace operator on closed surfaces ⋮ Numerical investigation of the properties of remainder in Gauss's circle problem
Cites Work
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- Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function
- On the Dirichlet divisor problem in short intervals
- On the divisor function and the Riemann zeta-function in short intervals
- On the divisor and circle problems
- New omega theorems for two classical lattice point problems
- Large values of the error term in the divisor problem
- Distribution of energy levels of a quantum free particle on a surface of revolution
- Sign changes of \(E(T)\), \(\Delta(x)\), and \(P(x)\)
- Moments over short intervals
- Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae
- Distribution of the error term for the number of lattice points inside a shifted circle
- On the higher moments of the error term in the divisor problem
- The changes of sign of certain arithmetical error-terms
- On the tails of the limiting distribution function of the error term in the Dirichlet divisor problem
- Bounds and behaviour of the quantities $ P(x)$, $ \Delta(x)$ on short intervals
- On the second term in the Weyl formula for the spectrum of the Laplace operator on the two-dimensional torus and the number of integer points in spectral domains
- Large values of certain number-theoretic error terms
- SPECTRAL THEORY OF AUTOMORPHIC FUNCTIONS, THE SELBERG ZETA-FUNCTION, AND SOME PROBLEMS OF ANALYTIC NUMBER THEORY AND MATHEMATICAL PHYSICS
- Exponential Sums and Lattice Points II
- Statistical properties of the spectra of Laplace-Beltrami operators on Liouville surfaces
- Exponential Sums and Lattice Points III
- On the divisor problem: Moments of Δ(x) over short intervals
- Lattice points in a circle: An improved mean-square asymptotics
- On higher-power moments of Δ(x) (II)
- The distribution and moments of the error term in the Dirichlet divisor problem
- Higher-Power Moments of δ(x ), E(t ) and P(x )