Quantum unique ergodicity for SL_2(Z)\H
By Kannan Soundararajan. 2009
166 citations recorded by the source corpus.
We eliminate the possibility of "escape of mass" for Hecke-Maass forms of large eigenvalue for the modular group. Combined with the work of Lindenstrauss, this establishes the Quantum Unique Ergodicity conjecture of Rudnick and Sarnak for the modular surface SL_2(Z)\H.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4eb88db38c733b2dc4ee3067fa0cd1d12b3970a9
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- M. Young
- Paul D. Nelson
- Kannan Soundararajan
- V. Blomer
- Rizwanur Khan
- R. Holowinsky
- Ian Petrow
- Peter Sarnak
In Mathematical Physics
- M. Young
- Paul D. Nelson
- Kannan Soundararajan
- V. Blomer
- Rizwanur Khan
- R. Holowinsky
- Ian Petrow
- Peter Sarnak
Citations in the corpus
- Weak subconvexity for central values of $L$-functions (2008, unknown): “This follows from the argument of Lemma 2.2 in Granville and Soundararajan [8].”
- Mass equidistribution for Hecke eigenforms (2008, background): “Recently the second author [16] showed that c D 1, completing the proof of the QUE conjecture for Hecke-Maass forms on SL2.”
- Distribution of mass of holomorphic cusp forms (2012, methodology): “s a crucial input for quantum unique ergodicity for Maaß forms on the modular surface; in essence it shows that mass (measured in the L2-sense) cannot escape through the cusp. However, the methods in [So], based on the properties of multiplicative functions, are very different from ours. Acknowledgem”
- Equidistribution Of Cusp Forms In The Level Aspect (2010, background): “We combine Theorem 3.1 and Theorem 4.1 with Soundararajan’s weak subconvex bounds [39] to complete the proof of Theorem 1.3.”