Sieving for mass equidistribution
By R. Holowinsky. 2008
62 citations recorded by the source corpus.
We approach the holomorphic analogue to the Quantum Unique Ergodicity conjecture through an application of the Large Sieve. We deal with shifted convolution sums as in [Ho109], with various simplifications in our analysis due to the knowledge of the Ramanujan-Petersson conjecture in this holomorphic case.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/930f60513a00bb7b48e02f89067aac2c8d397563
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In Algebra and Number Theory
- Paul D. Nelson
- P. Bourgade
- Kannan Soundararajan
- Horng-Tzer Yau
- Kevin Henriot
- R. Holowinsky
- L. Erdős
- M. Young
In Mathematical Physics
- Horng-Tzer Yau
- Paul D. Nelson
- L. Erdős
- P. Bourgade
- Kannan Soundararajan
- Jun Yin
- Ji Oon Lee
- Kevin Henriot
Citations in the corpus
- The Eigenvector Moment Flow and Local Quantum Unique Ergodicity (2013, background): “One case for which QUE was rigorously proved concerns arithmetic surfaces, thanks to tools from number theory and ergodic theory on homogeneous spaces [19,20,25].”
- A Dynamical Approach to Random Matrix Theory (2017, background): “One case for which QUE was rigorously proved concerns arithmetic surfaces, thanks to tools from number theory and ergodic theory on homogeneous spaces [81, 82, 100].”
- Equidistribution Of Cusp Forms In The Level Aspect (2010, methodology): “1, which in turn synthesizes the independent arguments of Holowinsky [14] and Soundararajan [39].”
- Mass equidistribution for Hecke eigenforms (2008, methodology): “The proof combines two different approaches to the mass equidistribution conjecture, developed independently by the authors [3], [17].”
- Nair–Tenenbaum bounds uniform with respect to the discriminant (2011, background): “Holowinsky’s approach [7] relies on estimates for shifted convolution sums ∑ n x λ f (n)λ f (n + ), where λ f are the renormalized Hecke eigenvalues of a Hecke eigencuspform f .”
- Weak subconvexity for central values of $L$-functions (2008, methodology): “Our criterion complements the work of Holowinsky [17], who attacks the mass equidistribution conjecture by an entirely different method.”