A Refined Gross-Prasad Conjecture for Unitary Groups

By Richard Harris. 2012

73 citations recorded by the source corpus.

Let F be a number field, AF its ring of adeles, and let [pi]n and [pi]n+1 be irreducible, cuspidal, automorphic representations of SOn(AF) and SOn+1AF), respectively. In 1991, Benedict Gross and Dipendra Prasad conjectured the non-vanishing of a certain period integral attached to [pi]n and [pi]n+1 is equivalent to the non-vanishing of L(1/2, [pi]n [X] [pi]n+1). More recently, Atsushi Ichino and Tamotsu Ikeda gave a refinement of this conjecture, as well as a proof of the first few cases (n = 2,3). Their conjecture gives an explicit relationship between the aforementioned L-value and period integral. We make a similar conjecture for unitary groups, and prove the first few cases. The first case of the conjecture will be proved using a theorem of Waldspurger, while the second case will use the machinery of the [theta] correspondence

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/86a5680dfe6079d565e2f06a6f4a31ae8c01c764

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. H. Grobner
2. Michael Harris
3. Wei Zhang
4. Chong-Quan Zhang

In Geometry and Topology

1. H. Grobner
2. Michael Harris
3. Wei Zhang
4. T. Gee
5. Peter Scholze
6. David Geraghty
7. Ana Caraiani
8. C. Skinner

In Mathematical Physics

1. H. Grobner
2. Michael Harris
3. Wei Zhang
4. T. Gee
5. Peter Scholze
6. David Geraghty
7. Ana Caraiani
8. C. Skinner

Citations in the corpus

• Automorphic period and the central value of Rankin--Selberg L-function (2012, background): “[23], [21]) that refines the global Gan–Gross–Prasad conjecture for unitary groups.”
• The orbit method and analysis of automorphic forms (2018, unknown): “See [43, 39].”
• WHITTAKER PERIODS, MOTIVIC PERIODS, AND SPECIAL VALUES OF TENSOR PRODUCT $L$ -FUNCTIONS (2013, methodology): “This is because they are based on Wei Zhang’s version [53] of the Ichino-IkedaNeal Harris conjecture for automorphic forms on unitary groups, see [20], and for the moment neither the local nor global properties of the relative trace formula are known in sufficient generality to allow a complete comp”