Equidistribution of cusp forms in the level aspect

DOI10.1215/00127094-144287zbMath1273.11069arXiv1011.1292OpenAlexW3098801381MaRDI QIDQ654872

Paul D. Nelson

Publication date: 23 December 2011

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

Full work available at URL: https://arxiv.org/abs/1011.1292

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)

Related Items

Bounds for eigenforms on arithmetic hyperbolic 3-manifolds, Zeros of Rankin-Selberg \(L\)-functions at the edge of the critical strip, Hybrid sup-norm bounds for Maass newforms of powerful level, Bounds for twisted symmetric square L-functions via half-integral weight periods, Zeros of newform Eisenstein series on \(\Gamma_{0}(N)\), Microlocal lifts and quantum unique ergodicity on \(\mathrm{GL}_2(\mathbb Q_p)\), Special value formula for the twisted triple product \(L\)-function and an application to the restricted \(L^2\)-norm problem, Quantum unique ergodicity for Eisenstein series in the level aspect, \(L^4\)-norms of Hecke newforms of large level, Some analytic aspects of automorphic forms on \(\mathrm{GL}(2)\) of minimal type, Quantum unique ergodicity for half-integral weight automorphic forms, Subconvex equidistribution of cusp forms: reduction to Eisenstein observables, Subconvexity and equidistribution of Heegner points in the level aspect, Mass equidistribution on the torus in the depth aspect, Pullbacks of Saito-Kurokawa lifts and a central value formula for degree 6 \(L\)-series, On Deligne's conjecture for certain automorphic \(L\)-Functions for \(\mathrm{GL}(3)\times\mathrm{GL}(2)\) and \(\mathrm{GL}(4)\), Bounds for Rankin–Selberg integrals and quantum unique ergodicity for powerful levels

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Decomposition of Eisenstein series: Rankin triple products
• Weak subconvexity for central values of \(L\)-functions
• Sieving for mass equidistribution
• Mass equidistribution for Hecke eigenforms
• Quantum unique ergodicity for \(\text{SL}_2(\mathbb Z)\setminus \mathbb H\)
• On functions of bounded (p,2)-variation
• The central critical value of a triple product \(L\)-function
• Trilinear forms and the central values of triple product \(L\)-functions
• Arithmétique des algèbres de quaternions
• The behaviour of eigenstates of arithmetic hyperbolic manifolds
• Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
• La conjecture de Weil. I
• Rankin-Selberg \(L\)-functions in the level aspect.
• Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\)
• On the periods of automorphic forms on special orthogonal groups and the Gross-Prasad conjecture
• Equidistribution of Eisenstein series in the level aspect
• Invariant measures and arithmetic unique ergodicity. Appendix by E. Lindenstrauss and D. Rudolph
• Hecke operators on \(\Gamma_0(m)\)
• Zeta functions of simple algebras
• Recent progress on the quantum unique ergodicity conjecture
• Multiplicative functions of polynomial values in short intervals
• On the Holomorphy of Certain Dirichlet Series
• Automorphic Forms on Adele Groups. (AM-83)
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• Mass equidistribution for Hecke eigenforms