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- Kuznetsov_trace_formula abstract "In analytic number theory, the Kuznetsov trace formula is an extension of the Petersson trace formula introduced in (Kuznetsov 1980).The Kuznetsov or relative trace formula connects Kloosterman sums at a deep level with the spectral theory of automorphic forms. Originally this could have been stated as follows. Let be a sufficiently "well behaved" function. Then one calls identities of the following type Kuznetsov trace formula:The integral transform part is some integral transform of g and the spectral part is a sum of Fourier coefficients, taken over spaces of holomorphic and non-holomorphic modular forms twisted with some integral transform of g. The Kuznetsov trace formula was found by Kuznetsov while studying the growth of weight zero automorphic functions. Using estimates on Kloosterman sums he was able to derive estimates for Fourier coefficients of modular forms in cases where Pierre Deligne's proof of the Weil conjectures was not applicable. It was later translated by Jacquet to a representation theoretic framework. Let be a reductive group over a number field F and be a subgroup. While the usual trace formula studies the harmonic analysis on G, the relative trace formula a tool for studying the harmonic analysis on the symmetric space . For an overview and numerous applications Cogdell, J.W. and I. Piatetski-Shapiro, The arithmetic and spectral analysis of Poincaré series, volume 13 of Perspectives in mathematics. Academic Press Inc., Boston, MA, (1990).".
- Kuznetsov_trace_formula wikiPageID "20484809".
- Kuznetsov_trace_formula wikiPageRevisionID "526604493".
- Kuznetsov_trace_formula hasPhotoCollection Kuznetsov_trace_formula.
- Kuznetsov_trace_formula subject Category:Analytic_number_theory.
- Kuznetsov_trace_formula comment "In analytic number theory, the Kuznetsov trace formula is an extension of the Petersson trace formula introduced in (Kuznetsov 1980).The Kuznetsov or relative trace formula connects Kloosterman sums at a deep level with the spectral theory of automorphic forms. Originally this could have been stated as follows. Let be a sufficiently "well behaved" function.".
- Kuznetsov_trace_formula label "Kuznetsov trace formula".
- Kuznetsov_trace_formula sameAs m.04_06ml.
- Kuznetsov_trace_formula sameAs Q6449272.
- Kuznetsov_trace_formula sameAs Q6449272.
- Kuznetsov_trace_formula wasDerivedFrom Kuznetsov_trace_formula?oldid=526604493.
- Kuznetsov_trace_formula isPrimaryTopicOf Kuznetsov_trace_formula.