+- Softwarez.Info - Software's World! (https://softwarez.info)
+-- Forum: Library Zone (https://softwarez.info/Forum-Library-Zone)
+--- Forum: E-Books (https://softwarez.info/Forum-E-Books)
+--- Thread: Vector-Valued Orthogonal Modular Forms (/Thread-Vector-Valued-Orthogonal-Modular-Forms)
Vector-Valued Orthogonal Modular Forms - ebooks1001 - 01-05-2026
![[Image: d771656986f231d2c4f2ffe6089dbe95.webp]](https://i126.fastpic.org/big/2026/0104/95/d771656986f231d2c4f2ffe6089dbe95.webp)
Free Download Vector-Valued Orthogonal Modular Forms
by Shouhei Ma
English | 2025 | ISBN: 3985475954 | 157 Pages | True PDF | 0.91 MB
This memoir is devoted to the theory of vector-valued modular forms for orthogonal groups of signature (2, n). Our purpose is multi-layered: (1) to lay a foundation of the theory of vector-valued orthogonal modular forms; (2) to develop some aspects of the theory in more depth such as geometry of the Siegel operators, filtrations associated to 1-dimensional cusps, decomposition of vector-valued Jacobi forms, square integrability etc; and (3) as applications derive several types of vanishing theorems for vector-valued modular forms of small weight. Our vanishing theorems imply in particular vanishing of holomorphic tensors of degree less than n/2-1 on orthogonal modular varieties, which is optimal as a general bound. The fundamental ingredients of the theory are the two Hodge bundles. The first is the Hodge line bundle which already appears in the theory of scalar-valued modular forms. The second Hodge bundle emerges in the vector-valued theory and plays a central role. It corresponds to the non-abelian part \mathrm{O}(n, \mathbb{R}) of the maximal compact subgroup of \mathrm{O}(2, n). The main focus of this monograph is centered around the properties and the role of the second Hodge bundle in the theory of vector-valued orthogonal modular forms.
Recommend Download Link Hight Speed | Please Say Thanks Keep Topic Live
Links are Interchangeable - Single Extraction