Rankin-Selberg $L$-functions in the level aspect

By Emmanuel Kowalski, P. Michel, Jeffrey M. Vanderkam. 2002

282 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5855c8c0c29e5e750b6de72aafda83127c06b79f

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. Akshay Venkatesh
3. Gergely Harcos
4. R. Munshi
5. Shou-wu Zhang
6. V. Blomer
7. Y. Lau
8. Emmanuel Kowalski

In Applied Mathematics

1. Akshay Venkatesh
2. Shou-wu Zhang
3. Gergely Harcos
4. Stephen D. Miller
5. P. Michel
6. W. Schmid
7. Jianya Liu
8. Yangbo Ye

In Mathematical Physics

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

Citations in the corpus

• Automorphic distributions, L-functions, and Voronoi summation for GL(3) (2004, background): “The Voronoi summation formula for GL(2) has become a fundamental analytic tool for a number of deep results in analytic number theory, most notably to the sub-convexity problem for automorphic L-functions; see [18] for a survey, as well as [10, 21,32].”
• An additive problem in the Fourier coefficients of cusp forms (2001, background): “Combining the estimate (4) at the central point s = 1/2 with Waldspurger’s theorem [Wa] (see also [ Ko ]) we get the bound”
• The subconvexity problem for GL2 (2009, background): “— The bound generalizes (up to the value of δ) a variety of subconvex bounds [71,12,29,27,47,17,18,64,22,34,19,42,44,48,6,54,31,9,8, 67,16].”
• Local spectral equidistribution for Siegel modular forms and applications (2010, background): “. • Computations tantamount to working with the twisted weight ω′ f are also classical (in particular, the computation of X f ω′ fλ (m) for a fixed mis a special case of the first moment computation in [30], in the case where the level goes to infinity and the Rankin-Selberg convolution is the weight 1”
• Summation formulas, from Poisson and Voronoi to the present (2003, methodology): “4.12 Theorem. [2,11, 15 ] If the Schwartz function f ∈ S(R) vanishes to infinite order at the origin,”
• GROSS-ZAGIER FORMULA FOR GL2 (2001, result): “If we further assume that the work [4] of Cogdell, Piateski-Shapiro, and Sarnak can be extended to unramified anticyclotomic characters which is predicted by GRH and (which holds over Q by recent work of Kowalski, Michel, and Vanderkam [27]), then our Gross-Zagier formula will imply the equidistribu”
• 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 subconvexity problem for Rankin–Selberg L-functions and equidistribution of Heegner points. II (2006, methodology): “Although these alternative approaches are very different from the ones coming from analytic number theory, an astute reader will nevertheless identify some common patterns on each side: this is especially striking when one compares [V05] with say [DFI94a] or [ KMV02 ].”