An additive problem in the Fourier coefficients of cusp forms
By Gergely Harcos. 2001
66 citations recorded by the source corpus.
Abstract. We establish an estimate on sums of shifted products of Fourier coefficients coming from holomorphic or Maass cusp forms of arbitrary level and nebentypus. These sums are analogous to the binary additive divisor sum which has been studied extensively. As an application we derive, extending work of Duke, Friedlander and Iwaniec, a subconvex estimate on the critical line for L-functions associated to character twists of these cusp forms.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7c54c4df2fe25c9c166c4e145dccdf9d4b3b5deb
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
- V. Blomer
- Akshay Venkatesh
- P. Michel
- Gergely Harcos
- R. Munshi
- M. Young
- Peter Sarnak
- Djordje Milićević
In Mathematical Physics
- V. Blomer
- P. Michel
- Akshay Venkatesh
- Gergely Harcos
- R. Munshi
- M. Young
- Peter Sarnak
- Djordje Milićević
Citations in the corpus
- The spectral decomposition of shifted convolution sums (2007, methodology): “In the general case, variants of the circle method with the Kloosterman refinement have been particularly successful (see[DFI1],[DFI2],[Ju2],[ H1 ],[HM],[B],[BHM]).”
- The subconvexity problem for Rankin–Selberg L-functions and equidistribution of Heegner points. II (2006, methodology): “During the two years of this project, J. Friedlander, H . Iwaniec and P. Sarnak generously shared with me their experience, ideas and even the manuscripts (from the roughest to the most polished versions) of their respective ongoing projects; I thank them heartily for this, for their encouragement ”
- Shifted convolution sums and subconvexity bounds for automorphic L-functions (2004, background): “Harcos’ paper [10] yields such a result for h ≤ M while variants of the δ-method (see [1, 5]) give uniformity up to h ≤M3/2−ε.”
- Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik (2006, methodology): “3) or Jutila’s method of overleaping intervals which is particularly flexible [38], [45].”