"1994-02-01" .
_:N833a1dcc8672443f8080b0afbb7906b5 "dimensions_id" .
.
.
.
_:N89f44525b227462eb9d94ee412c87868 .
.
.
_:N097ad8fe45ad4c75a15c035c49e05069 .
.
.
_:N097ad8fe45ad4c75a15c035c49e05069 "doi" .
.
_:N07f88542e6cf4019a87e78481e59ab05 .
_:N7095a90c6733473fa8b683f84e699966 "readcube_id" .
.
_:N335a9fb6ff9c4e4cb4e29ff4a96b45f3 .
_:Nee5fed02c66b4ecb9838e4dd13c1c3af .
"false"^^ .
"Max Planck Institute for Mathematics" .
.
.
_:N7095a90c6733473fa8b683f84e699966 .
"Max-Planck-Institut f\u00FCr Mathematik, Gottfried-Claren Str. 26, 53225, Bonn, Germany" .
"Don" .
.
.
.
.
.
_:N335a9fb6ff9c4e4cb4e29ff4a96b45f3 "Springer Nature - SN SciGraph project" .
_:Nee5fed02c66b4ecb9838e4dd13c1c3af .
"http://link.springer.com/10.1007/BF02830874" .
_:N097ad8fe45ad4c75a15c035c49e05069 .
"en" .
"Zagier" .
_:N833a1dcc8672443f8080b0afbb7906b5 .
_:N07f88542e6cf4019a87e78481e59ab05 .
.
"1994-02" .
_:N07f88542e6cf4019a87e78481e59ab05 "104" .
_:N335a9fb6ff9c4e4cb4e29ff4a96b45f3 .
"2019-04-11T13:35" .
.
_:N7095a90c6733473fa8b683f84e699966 .
.
"Modular forms and differential operators" .
"Mathematical Sciences" .
.
"Proceedings - Mathematical Sciences" .
.
"2251-7456" .
_:N89f44525b227462eb9d94ee412c87868 .
_:N7095a90c6733473fa8b683f84e699966 "0ddd5305253cc6c98a61727dfe6537b020a44642d296b5f3eea3c68f8be4e6a8" .
_:Nee5fed02c66b4ecb9838e4dd13c1c3af .
.
.
"57-75" .
"articles" .
.
_:N097ad8fe45ad4c75a15c035c49e05069 "10.1007/bf02830874" .
"2008-1359" .
"research_article" .
.
"In 1956, Rankin described which polynomials in the derivatives of modular forms are again modular forms, and in 1977, H Cohen defined for eachn \u2265 0 a bilinear operation which assigns to two modular formsf andg of weightk andl a modular form [f, g]n of weightk +l + 2n. In the present paper we study these \u201CRankin-Cohen brackets\u201D from two points of view. On the one hand we give various explanations of their modularity and various algebraic relations among them by relating the modular form theory to the theories of theta series, of Jacobi forms, and of pseudodifferential operators. In a different direction, we study the abstract algebraic structure (\u201CRC algebra\u201D) consisting of a graded vector space together with a collection of bilinear operations [,]n of degree + 2n satisfying all of the axioms of the Rankin-Cohen brackets. Under certain hypotheses, these turn out to be equivalent to commutative graded algebras together with a derivationS of degree 2 and an element \u03A6 of degree 4, up to the equivalence relation (\u2202,\u03A6) ~ (\u2202 - \u03D5E, \u03A6 - \u03D52 + \u2202(\u03D5)) where \u03D5 is an element of degree 2 andE is the Fuler operator (= multiplication by the degree)." .
.
.
_:N89f44525b227462eb9d94ee412c87868 "1" .
_:N833a1dcc8672443f8080b0afbb7906b5 "pub.1002910991" .
.
_:N833a1dcc8672443f8080b0afbb7906b5 .
.
.
"https://scigraph.springernature.com/explorer/license/" .
"Pure Mathematics" .