The subconvexity problem for Rankin-Selberg L-functions and equidistribution of Heegner points

By P. Michel. 2004

255 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/719d7672e67263ec12247aabfbd082915a7d5cf9

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

1. R. Munshi
2. P. Michel
3. V. Blomer
4. Akshay Venkatesh
5. Gergely Harcos
6. Shou-wu Zhang
7. Nicolas Templier
8. Y. Lau

In Applied Mathematics

1. Akshay Venkatesh
2. V. Blomer
3. Manfred Einsiedler
4. Shou-wu Zhang
5. R. Munshi
6. Nicolas Templier
7. P. Michel
8. Gergely Harcos

In Geometry and Topology

1. Akshay Venkatesh
2. P. Michel
3. V. Blomer
4. Gergely Harcos
5. R. Munshi
6. Manfred Einsiedler
7. Shou-wu Zhang
8. Nicolas Templier

Citations in the corpus

• The circle method and bounds for L-functions---II: Subconvexity for twists of GL(3) L-functions (2012, methodology): “The first subconvex bound in theM aspect (for t = 0) was obtained by Duke, Friedlander and Iwaniec [7] (for holomorphic forms of full level), Bykovskii [4] (for general holomorphic forms) and later by Harcos [9], Michel [15] and Blomer, Harcos and Michel [3] (for Maass forms).”
• A new bound K2/3+ɛ for Rankin-Selberg ℒ-functions for Hecke congruence subgroups (2010, background): “Interested readers are referred to the important works of Kowalski, Michel and VanderKam [20], Michel [26], and Harcos and Michel [11].”
• On the Voronoĭ formula for GL(n) (2013, methodology): “The Vorono˘ı formula for GL ( 2 ) is a basic tool for the study of analytic properties of automorphic forms, see the series of papers by Duke-Friedlander-Iwaniec [5] or Kowalski-Michel-VanderKam [25] and Harcos-Michel [15], and the references there.”
• The distribution of periodic torus orbits on homogeneous spaces (2006, background): “These results use (in addition to, respectively, the results of [17] and the GRH) the relationship between torus orbits and Rankin-Selberg L-functions, established in the work of Waldspurger, Katok-Sarnak and Popa (see e.”
• Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik (2006, methodology): “The case of Rankin/Selberg L-functions over Q, L(π1 × π2, s) when π2 is essentially fixed and π1 has a central character ω1 of large conductor was treated in [39,60].”
• Sparse equidistribution problems, period bounds and subconvexity (2005, methodology): “Examples of this type of question are Shah’s conjecture [38, 1, end] (where the Zi are discrete subsets of Yi , a full horocycle orbit) as well as results of Michel, Harcos-Michel on subsets of Heegner points [27], [17] (where the Zi are subsets of the Yi , the set of all Heegner points).”
• Shifted convolution sums and subconvexity bounds for automorphic L-functions (2004, background): “If we choose θ = 1/4, we get back the exponent 5/11 = 0.4545 . . . of Duke, Friedlander, Iwaniec, and Michel.”