Large values of eigenfunctions on arithmetic hyperbolic surfaces

DOI10.1215/00127094-2010-058zbMath1219.11071OpenAlexW2028417310MaRDI QIDQ616588

Djordje Milićević

Publication date: 10 January 2011

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/00127094-2010-058

zbMATH Keywords

large valuesarithmetic hyperbolic surfaceCM-pointHecke-Maass eigenform

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Modular correspondences, etc. (11F32) Rate of growth of arithmetic functions (11N56) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)

Related Items (12)

The L² restriction norm of a GL₃ Maass form ⋮ From nodal points to non-equidistribution at the Planck scale ⋮ The \(L^2\) restriction norm of a Maass form on \(\mathrm{SL}_{n+1}(\mathbb {Z})\) ⋮ Equidistribution in shrinking sets and \(L^4\)-norm bounds for automorphic forms ⋮ Analytic properties of spherical cusp forms on \(\mathrm{GL}(n)\) ⋮ EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES ⋮ The distribution of values of zeta and \(L\)-functions ⋮ Large values of eigenfunctions on arithmetic hyperbolic 3-manifolds ⋮ Entropy bounds and quantum unique ergodicity for Hecke eigenfunctions on division algebras ⋮ Small scale equidistribution of eigenfunctions on the torus ⋮ Triple product \(L\)-functions and quantum chaos on \(\mathrm{SL}(2,\mathbb C)\) ⋮ Arithmetic, zeros, and nodal domains on the sphere

Cites Work

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• Quantum unique ergodicity for \(\text{SL}_2(\mathbb Z)\setminus \mathbb H\)
• Bounding sup-norms of cusp forms of large level
• Extreme values of zeta and \(L\)-functions
• Hyperbolic distribution problems and half-integral weight Maass forms
• A characterization of arithmetic Fuchsian groups
• Heegner points, cycles and Maass forms
• The subconvexity problem for \(\mathrm{GL}_2\)
• \(L^ \infty\) norms of eigenfunctions of arithmetic surfaces
• A geometric characterization of arithmetic Fuchsian groups.
• Invariant measures and arithmetic unique ergodicity. Appendix by E. Lindenstrauss and D. Rudolph
• Topics in multiplicative number theory
• On the Topography of Maass Waveforms for PSL(2, Z)
• Über die Darstellbarkeit von Modulformen durch Thetareihen.
• On the Decomposition of a Representation of SO_n When Restricted to SO_n-1
• Regular and irregular semiclassical wavefunctions
• The Fourth Power Moment of the Riemann Zeta Function
• Band-Limited Wavelets with Subexponential Decay
• The Mean Square of the Error Term for the Fourth Power Moment of the Zeta-Function
• The maximum size of L-functions

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