The Theory of Jacobi Forms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser Boston
1985
|
| Series: | Progress in Mathematics
55 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper half-plane) satisfying the t\-10 transformation eouations 2Tiimcz· k CT +d a-r +b z ) (1) ( (cT+d) e cp(T,z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Four·ier expansion of the form 00 e2Tii(nT +rz) (3) cp(T,z) 2: c(n,r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z-+rjl(-r,z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)-(3) arise classically: 1. Theta series. Let Q: ~-+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form |
| Physical Description: | 1 Online-Ressource (V, 150 p) |
| ISBN: | 9781468491623 9781468491647 |
| ISSN: | 0743-1643 |
| DOI: | 10.1007/978-1-4684-9162-3 |
Staff View
MARC
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| 245 | 1 | 0 | |a The Theory of Jacobi Forms |c by Martin Eichler, Don Zagier |
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| 500 | |a The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper half-plane) satisfying the t\-10 transformation eouations 2Tiimcz· k CT +d a-r +b z ) (1) ( (cT+d) e cp(T,z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Four·ier expansion of the form 00 e2Tii(nT +rz) (3) cp(T,z) 2: c(n,r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z-+rjl(-r,z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)-(3) arise classically: 1. Theta series. Let Q: ~-+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Geometry, algebraic | |
| 650 | 4 | |a Group theory | |
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| 650 | 4 | |a Number theory | |
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| 650 | 4 | |a Algebraic Geometry | |
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Record in the Search Index
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| any_adam_object | |
| author | Eichler, Martin 1912-1992 |
| author_GND | (DE-588)117709751 (DE-588)120415569 |
| author_facet | Eichler, Martin 1912-1992 |
| author_role | aut |
| author_sort | Eichler, Martin 1912-1992 |
| author_variant | m e me |
| building | Verbundindex |
| bvnumber | BV042421163 |
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| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-9162-3 |
| format | Electronic eBook |
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| id | DE-604.BV042421163 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468491623 9781468491647 |
| issn | 0743-1643 |
| language | English |
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| physical | 1 Online-Ressource (V, 150 p) |
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| publishDate | 1985 |
| publishDateSearch | 1985 |
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| publisher | Birkhäuser Boston |
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| series2 | Progress in Mathematics |
| spelling | Eichler, Martin 1912-1992 Verfasser (DE-588)117709751 aut The Theory of Jacobi Forms by Martin Eichler, Don Zagier Boston, MA Birkhäuser Boston 1985 1 Online-Ressource (V, 150 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 55 0743-1643 The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper half-plane) satisfying the t\-10 transformation eouations 2Tiimcz· k CT +d a-r +b z ) (1) ( (cT+d) e cp(T,z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Four·ier expansion of the form 00 e2Tii(nT +rz) (3) cp(T,z) 2: c(n,r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z-+rjl(-r,z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)-(3) arise classically: 1. Theta series. Let Q: ~-+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form Mathematics Geometry, algebraic Group theory Functional analysis Number theory Number Theory Algebraic Geometry Group Theory and Generalizations Functional Analysis Mathematik Elliptische Funktion (DE-588)4134665-8 gnd rswk-swf Jacobi-Form (DE-588)4319811-9 gnd rswk-swf Modulform (DE-588)4128299-1 gnd rswk-swf Holomorphe Funktion (DE-588)4025645-5 gnd rswk-swf Jacobische elliptische Funktion (DE-588)4162644-8 gnd rswk-swf Holomorphe Funktion (DE-588)4025645-5 s Elliptische Funktion (DE-588)4134665-8 s 1\p DE-604 Modulform (DE-588)4128299-1 s 2\p DE-604 Jacobische elliptische Funktion (DE-588)4162644-8 s 3\p DE-604 Jacobi-Form (DE-588)4319811-9 s 4\p DE-604 Zagier, Don 1951- Sonstige (DE-588)120415569 oth https://doi.org/10.1007/978-1-4684-9162-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Eichler, Martin 1912-1992 The Theory of Jacobi Forms Mathematics Geometry, algebraic Group theory Functional analysis Number theory Number Theory Algebraic Geometry Group Theory and Generalizations Functional Analysis Mathematik Elliptische Funktion (DE-588)4134665-8 gnd Jacobi-Form (DE-588)4319811-9 gnd Modulform (DE-588)4128299-1 gnd Holomorphe Funktion (DE-588)4025645-5 gnd Jacobische elliptische Funktion (DE-588)4162644-8 gnd |
| subject_GND | (DE-588)4134665-8 (DE-588)4319811-9 (DE-588)4128299-1 (DE-588)4025645-5 (DE-588)4162644-8 |
| title | The Theory of Jacobi Forms |
| title_auth | The Theory of Jacobi Forms |
| title_exact_search | The Theory of Jacobi Forms |
| title_full | The Theory of Jacobi Forms by Martin Eichler, Don Zagier |
| title_fullStr | The Theory of Jacobi Forms by Martin Eichler, Don Zagier |
| title_full_unstemmed | The Theory of Jacobi Forms by Martin Eichler, Don Zagier |
| title_short | The Theory of Jacobi Forms |
| title_sort | the theory of jacobi forms |
| topic | Mathematics Geometry, algebraic Group theory Functional analysis Number theory Number Theory Algebraic Geometry Group Theory and Generalizations Functional Analysis Mathematik Elliptische Funktion (DE-588)4134665-8 gnd Jacobi-Form (DE-588)4319811-9 gnd Modulform (DE-588)4128299-1 gnd Holomorphe Funktion (DE-588)4025645-5 gnd Jacobische elliptische Funktion (DE-588)4162644-8 gnd |
| topic_facet | Mathematics Geometry, algebraic Group theory Functional analysis Number theory Number Theory Algebraic Geometry Group Theory and Generalizations Functional Analysis Mathematik Elliptische Funktion Jacobi-Form Modulform Holomorphe Funktion Jacobische elliptische Funktion |
| url | https://doi.org/10.1007/978-1-4684-9162-3 |
| work_keys_str_mv | AT eichlermartin thetheoryofjacobiforms AT zagierdon thetheoryofjacobiforms |