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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:category
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Eigenfunctions of invariant differential operators
Functions on locally symmetric spaces
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gptkbp:defines
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A complex-valued function on a topological group that is invariant under the action of a discrete subgroup, up to a character.
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gptkbp:field
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gptkb:Mathematics
gptkb:Number_theory
gptkb:Representation_theory
Harmonic analysis
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gptkbp:firstAppearance
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Early 20th century
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gptkbp:generalizes
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gptkb:Modular_forms
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https://www.w3.org/2000/01/rdf-schema#label
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Automorphic forms
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gptkbp:notableFor
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gptkb:Trace_formula
Modularity theorem
Proof of Fermat's Last Theorem
Reciprocity laws
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gptkbp:relatedTo
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gptkb:Taniyama–Shimura–Weil_conjecture
gptkb:Bianchi_modular_forms
gptkb:Cusp_forms
gptkb:Drinfeld_modular_forms
gptkb:Hasse–Weil_L-function
gptkb:Hilbert_modular_forms
gptkb:Jacobi_forms
gptkb:Eisenstein_series
gptkb:Langlands_program
gptkb:Langlands_dual_group
gptkb:Arthur–Selberg_trace_formula
gptkb:Maass_forms
gptkb:Modular_forms
gptkb:Shimura_varieties
gptkb:Siegel_modular_forms
gptkb:Automorphic_L-functions
gptkb:Sato–Tate_conjecture
gptkb:Ramanujan_conjecture
Hecke operators
Galois representations
Automorphic representations
Functoriality principle
Theta functions
Adelic groups
Reductive algebraic groups
Representation of GL(n)
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gptkbp:studiedBy
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gptkb:Atle_Selberg
gptkb:Erich_Hecke
gptkb:Robert_Langlands
gptkb:Goro_Shimura
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gptkbp:usedIn
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gptkb:Langlands_correspondence
L-functions
Arithmetic geometry
Spectral theory
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gptkbp:bfsParent
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gptkb:L-functions_and_automorphic_representations
gptkb:Epstein_zeta_function
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gptkbp:bfsLayer
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5
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