�ݺ�ߣshows by User: AliAjouz

�ݺ�ߣshows by User: AliAjouz / http://www.slideshare.net/images/logo.gif �ݺ�ߣshows by User: AliAjouz / Sat, 22 Apr 2017 02:44:20 GMT �ݺ�ߣShare feed for �ݺ�ߣshows by User: AliAjouz Hecke Operators on Jacobi Forms of Lattice Index and the Relation to Elliptic Modular Forms /slideshow/hecke-operators-on-jacobi-forms-of-lattice-index-and-the-relation-to-elliptic-modular-forms/75295936 defence-170422024421
Jacobi forms of lattice index, whose theory can be viewed as extension of the theory of classical Jacobi forms, play an important role in various theories, like the theory of orthogonal modular forms or the theory of vertex operator algebras. Every Jacobi form of lattice index has a theta expansion which implies, for index of odd rank, a connection to half integral weight modular forms and then via Shimura lifting to modular forms of integral weight, and implies a direct connection to modular forms of integral weight if the rank is even. The aim of this thesis is to develop a Hecke theory for Jacobi forms of lattice index extending the Hecke theory for the classical Jacobi forms, and to study how the indicated relations to elliptic modular forms behave under Hecke operators. After defining Hecke operators as double coset operators, we determine their action on the Fourier coefficients of Jacobi forms, and we determine the multiplicative relations satisfied by the Hecke operators, i.e. we study the structural constants of the algebra generated by the Hecke operators. As a consequence we show that the vector space of Jacobi forms of lattice index has a basis consisting of simultaneous eigenforms for our Hecke operators, and we discover the precise relation between our Hecke algebras and the Hecke algebras for modular forms of integral weight. The latter supports the expectation that there exist equivariant isomorphisms between spaces of Jacobi forms of lattice index and spaces of integral weight modular forms. We make this precise and prove the existence of such liftings in certain cases. Moreover, we give further evidence for the existence of such liftings in general by studying numerical examples.]]>
Jacobi forms of lattice index, whose theory can be viewed as extension of the theory of classical Jacobi forms, play an important role in various theories, like the theory of orthogonal modular forms or the theory of vertex operator algebras. Every Jacobi form of lattice index has a theta expansion which implies, for index of odd rank, a connection to half integral weight modular forms and then via Shimura lifting to modular forms of integral weight, and implies a direct connection to modular forms of integral weight if the rank is even. The aim of this thesis is to develop a Hecke theory for Jacobi forms of lattice index extending the Hecke theory for the classical Jacobi forms, and to study how the indicated relations to elliptic modular forms behave under Hecke operators. After defining Hecke operators as double coset operators, we determine their action on the Fourier coefficients of Jacobi forms, and we determine the multiplicative relations satisfied by the Hecke operators, i.e. we study the structural constants of the algebra generated by the Hecke operators. As a consequence we show that the vector space of Jacobi forms of lattice index has a basis consisting of simultaneous eigenforms for our Hecke operators, and we discover the precise relation between our Hecke algebras and the Hecke algebras for modular forms of integral weight. The latter supports the expectation that there exist equivariant isomorphisms between spaces of Jacobi forms of lattice index and spaces of integral weight modular forms. We make this precise and prove the existence of such liftings in certain cases. Moreover, we give further evidence for the existence of such liftings in general by studying numerical examples.]]> Sat, 22 Apr 2017 02:44:20 GMT /slideshow/hecke-operators-on-jacobi-forms-of-lattice-index-and-the-relation-to-elliptic-modular-forms/75295936 AliAjouz@slideshare.net(AliAjouz) Hecke Operators on Jacobi Forms of Lattice Index and the Relation to Elliptic Modular Forms AliAjouz Jacobi forms of lattice index, whose theory can be viewed as extension of the theory of classical Jacobi forms, play an important role in various theories, like the theory of orthogonal modular forms or the theory of vertex operator algebras. Every Jacobi form of lattice index has a theta expansion which implies, for index of odd rank, a connection to half integral weight modular forms and then via Shimura lifting to modular forms of integral weight, and implies a direct connection to modular forms of integral weight if the rank is even. The aim of this thesis is to develop a Hecke theory for Jacobi forms of lattice index extending the Hecke theory for the classical Jacobi forms, and to study how the indicated relations to elliptic modular forms behave under Hecke operators. After defining Hecke operators as double coset operators, we determine their action on the Fourier coefficients of Jacobi forms, and we determine the multiplicative relations satisfied by the Hecke operators, i.e. we study the structural constants of the algebra generated by the Hecke operators. As a consequence we show that the vector space of Jacobi forms of lattice index has a basis consisting of simultaneous eigenforms for our Hecke operators, and we discover the precise relation between our Hecke algebras and the Hecke algebras for modular forms of integral weight. The latter supports the expectation that there exist equivariant isomorphisms between spaces of Jacobi forms of lattice index and spaces of integral weight modular forms. We make this precise and prove the existence of such liftings in certain cases. Moreover, we give further evidence for the existence of such liftings in general by studying numerical examples. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/defence-170422024421-thumbnail.jpg?width=120&height=120&fit=bounds" /><br> Jacobi forms of lattice index, whose theory can be viewed as extension of the theory of classical Jacobi forms, play an important role in various theories, like the theory of orthogonal modular forms or the theory of vertex operator algebras. Every Jacobi form of lattice index has a theta expansion which implies, for index of odd rank, a connection to half integral weight modular forms and then via Shimura lifting to modular forms of integral weight, and implies a direct connection to modular forms of integral weight if the rank is even. The aim of this thesis is to develop a Hecke theory for Jacobi forms of lattice index extending the Hecke theory for the classical Jacobi forms, and to study how the indicated relations to elliptic modular forms behave under Hecke operators. After defining Hecke operators as double coset operators, we determine their action on the Fourier coefficients of Jacobi forms, and we determine the multiplicative relations satisfied by the Hecke operators, i.e. we study the structural constants of the algebra generated by the Hecke operators. As a consequence we show that the vector space of Jacobi forms of lattice index has a basis consisting of simultaneous eigenforms for our Hecke operators, and we discover the precise relation between our Hecke algebras and the Hecke algebras for modular forms of integral weight. The latter supports the expectation that there exist equivariant isomorphisms between spaces of Jacobi forms of lattice index and spaces of integral weight modular forms. We make this precise and prove the existence of such liftings in certain cases. Moreover, we give further evidence for the existence of such liftings in general by studying numerical examples.

Hecke Operators on Jacobi Forms of Lattice Index and the Relation to Elliptic Modular Forms from Ali Ajouz

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0 SAS cheat sheet /slideshow/sas-cheat-sheet/74169536 sascheatsheet-170401221255
A SAS Language Mini Reference]]>
A SAS Language Mini Reference]]> Sat, 01 Apr 2017 22:12:55 GMT /slideshow/sas-cheat-sheet/74169536 AliAjouz@slideshare.net(AliAjouz) SAS cheat sheet AliAjouz A SAS Language Mini Reference <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/sascheatsheet-170401221255-thumbnail.jpg?width=120&height=120&fit=bounds" /><br> A SAS Language Mini Reference

SAS cheat sheet from Ali Ajouz

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0 https://public.slidesharecdn.com/v2/images/profile-picture.png https://cdn.slidesharecdn.com/ss_thumbnails/defence-170422024421-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/hecke-operators-on-jacobi-forms-of-lattice-index-and-the-relation-to-elliptic-modular-forms/75295936 Hecke Operators on Jac... https://cdn.slidesharecdn.com/ss_thumbnails/sascheatsheet-170401221255-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/sas-cheat-sheet/74169536 SAS cheat sheet