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- Title
Special Values of L-functions for GL(n) Over a CM Field.
- Authors
Raghuram, A
- Abstract
We prove a Galois-equivariant algebraicity result for the ratios of successive critical values of |$L$| -functions for |${\textrm GL}(n)/F,$| where |$F$| is a totally imaginary quadratic extension of a totally real number field |$F^+$|. The proof uses (1) results of Arthur and Clozel on automorphic induction from |${\textrm GL}(n)/F$| to |${\textrm GL}(2n)/F^+$| , (2) results of my work with Harder on ratios of critical values for |$L$| -functions of |${\textrm GL}(2n)/F^+$| , and (3) period relations amongst various automorphic and cohomological periods for |${\textrm GL}(2n)/F^+$| using my work with Shahidi. The reciprocity law inherent in the algebraicity result is exactly as predicted by Deligne's conjecture on the special values of motivic |$L$| -functions.
- Subjects
L-functions; REAL numbers; AUTOMORPHIC functions; DEDEKIND sums
- Publication
IMRN: International Mathematics Research Notices, 2022, Vol 2022, Issue 13, p10119
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnaa383