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

By Gergely Harcos, P. Michel. 2006

194 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7c7bf1f2593ba5f7f0233b3388126ed81f7591d6

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

In Geometry and Topology

1. V. Blomer
2. M. Young
3. Gergely Harcos
4. P. Michel
5. Akshay Venkatesh
6. Shou-wu Zhang
7. Y. Lau
8. Jianya Liu

In Mathematical Physics

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

Citations in the corpus

• Shifted convolution sums and subconvexity bounds for automorphic L-functions (2004, methodology): “This has applications to the subconvexity problem for Rankin-Selberg L-functions, see [11].”
• Bounding sup-norms of cusp forms of large level (2008, unknown): “> 1+|s|2, (23) cosh(πt/2)Ks(y) ≪ε,σ ˆ ((1+ |t|)y−1) |σ +ε, y 6 1+ 1 2π|t| e−y+π|t|/2y−1/2, y > 1+ 1 2π |t ˙ ≪A 1+|t| y |σ|+ε 1+ y 1+|t| −A . The estimates (21) - (23) follow directly from [HM], Propositions 8 and 9. They are not best possible in all ranges, but sufficiently uniform for our pre”
• The subconvexity problem for GL2 (2009, background): “The phenomenon of reduction to another case of subconvexity was noted by the first-named author in [48].”
• 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].”
• The spectral decomposition of shifted convolution sums (2007, background): “sions enable considerable simplifications in arguments leading to subconvexity results such as (6) which appeared originally in [BHM] or the more difficult case of Rankin–Selberg L-functions treated in [HM]. In this paper we have decided to present the theorems in a special case in order to keep the n”
• Weyl-type hybrid subconvexity bounds for twisted $L$-functions and Heegner points on shrinking sets (2014, methodology): “re we directly relate a sum over Heegner points to central L-values, which is provided by a formula of Waldspurger/Zhang [W] [Z], similarly to the style of proof of Harcos and 4 MATTHEWP.YOUNG Michel [HM]. Suppose that uj is a Hecke-Maass cusp form, orthonormalized with dxdy y2 (not probability meas”
• Sparse equidistribution problems, period bounds and subconvexity (2005, methodology): “we wish to deduce the equidistribution of the “sparse” subset Zi from the known equidistribution of Yi. Examples of this type of question are Shah’s conjecture [32] (where the Zi are discrete subsets of Yi, a full horocycle orbit) as well as Michel’s results on subsets of Heegner points [ 22 ] (wher”
• Equidistribution of CM-points on quaternion Shimura varieties (2005, methodology): “When F = Q, the subconvexity has been proven by Michel [20] for holomorphic forms f with δ = 1/2 − 1/1145, and by Harcos and Michel [16] for mass forms fwith δ = 1/2− 1/2491.”