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y
The metaplectic covering Mp(2n) of Sp(2n) affords an accessible yet nontrivial instance of the Langlands-Weissman program for covering groups. In order to use Arthur's methods in this setting, one needs a stable trace formula for Mp(2n). Thus far, only the elliptic terms have been stabilized. In this talk, I will report an ongoing work on the full stabilization, which is nearing completion. It will hopefully grant access to the whole genuine discrete automorphic spectrum of Mp(2n). Time permitting, I will also try to explain the similarities and subtle differences with the case of linear groups solved by Arthur.
[-] The metaplectic covering Mp(2n) of Sp(2n) affords an accessible yet nontrivial instance of the Langlands-Weissman program for covering groups. In order to use Arthur's methods in this setting, one needs a stable trace formula for Mp(2n). Thus far, only the elliptic terms have been stabilized. In this talk, I will report an ongoing work on the full stabilization, which is nearing completion. It will hopefully grant access to the whole genuine ...
[+] 22E50 ; 11F70 ; 11F72
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y
In this talk, we consider the limit multiplicity question (and some variants): how many automorphic forms of fixed infinity-type and level N are there as N grows? The question is well-understood when the archimedean representation is a discrete series, and we focus on non-tempered cohomological representations on unitary groups. Using an inductive argument which relies on the stabilization of the trace formula and the endoscopic classification, we give asymptotic counts of multiplicities, and prove the Sarnak-Xue conjecture at split level for (almost!) all cohomological representations of unitary groups. Additionally, for some representations, we derive an average Sato-Tate result in which the measure is the one predicted by functoriality. This is joint work with Rahul Dalal.
[-] In this talk, we consider the limit multiplicity question (and some variants): how many automorphic forms of fixed infinity-type and level N are there as N grows? The question is well-understood when the archimedean representation is a discrete series, and we focus on non-tempered cohomological representations on unitary groups. Using an inductive argument which relies on the stabilization of the trace formula and the endoscopic classification, ...
[+] 11F55 ; 11F70 ; 11F72 ; 11F75 ; 22E50
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y
The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the deep structure of L-functions and also provides insights into advanced conjectures such as the Riemann hypothesis.
[-] The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the ...
[+] 11M41 ; 11F66 ; 11F72
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y
The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the deep structure of L-functions and also provides insights into advanced conjectures such as the Riemann hypothesis.
[-] The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the ...
[+] 11M41 ; 11F66 ; 11F72
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English
