The theory of jacobi forms
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A Jacobi form of level 1, weight k and index m is a function $${\displaystyle \phi (\tau ,z)}$$ of two complex variables (with τ in the upper half plane) such that $${\displaystyle \phi \left({\frac {a\tau +b}{c\tau +d}},{\frac {z}{c\tau +d}}\right)=(c\tau +d)^{k}e^{\frac {2\pi imcz^{2}}{c\tau +d}}\phi … See more In mathematics, a Jacobi form is an automorphic form on the Jacobi group, which is the semidirect product of the symplectic group Sp(n;R) and the Heisenberg group $${\displaystyle H_{R}^{(n,h)}}$$. … See more Examples in two variables include Jacobi theta functions, the Weierstrass ℘ function, and Fourier–Jacobi coefficients of Siegel modular forms of … See more WebJun 9, 2006 · The theory of Jacobi forms was established by Eichler and Zagier [2], and, using it, they clarified and extended Maass' results [7] on the "Saito-Kurokawa conjecture" and related works given by several mathematicians. The most basic examples of Jacobi forms are Fourier-Jacobi coefficients of
The theory of jacobi forms
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WebIn this paper we develop ideas and previous results on cohomology of Jacobi forms originating from algebraic and geometrical procedures in conformal field theory [FS, TUY]. This paper aims at developing algebraic, differential geometry, and topological methods for the investigation of cohomology theories of Jacobi forms generated by WebSep 14, 2013 · The Theory of Jacobi Forms. Martin Eichler, Don Zagier. Birkhäuser Boston, Sep 14, 2013 - Mathematics - 150 pages. 0 Reviews. Reviews aren't verified, but Google …
WebApr 1, 1994 · The theory of Jacobi forms on H × C 8 (or over Cayley numbers) was initiated by Eie ( [3]) and A. Krieg ([4, 5]) in 1991 to investigate modular forms which lie in the Maass space on the upper ... WebThe Theory of Jacobi Forms - Ebook written by Martin Eichler, Don Zagier. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline …
WebThe Theory of Jacobi Forms over the Cayley Numbers. The Theory of Jacobi Forms over the Cayley Numbers. Aloys Krieg. 1994, Transactions of the American Mathematical Society. Read Full Text Download PDF. Read Full Text Download PDF. Related Papers. Kac-Moody algebras, the Monstrous Moonshine, Jacobi forms and infinite products. WebWe consider two classes of Jacobi matrix operators in l2 with zero diagonals and with weights of the form nα + cn for 0 < α ≤ 1 or of the form nα + cnnα-1 for α > 1, where {cn} is periodic. We study spectral properties of these operators (especially for ...
WebThe theory of p-adic modular forms was developed by J.-P. Serre [8] and N. Katz [5]. This theory is by now considered classical. Investigation of p-adic congruences for modular forms of half-integer weight was carried out by N. Koblitz [6] and led him to deep conjectures. It seems natural to search for p-adic properties of other types of …
Web210 Jae-Hyun Yang provide you with some characterizations of singular Jacobi forms due to Yang [85]. We roughly explain that the study of singular Jacobi forms is closely related to the invariant theory of the action of the group GL(g,R) ⋉ H(g,h) R (cf. (9.1)) and to the geometry of the universal abelian variety. intensive outpatient clinic west valleyhttp://maths.inha.ac.kr/~jhyang/paper/GTJacobi-KMJ.pdf intensive online arabic courseWebMar 15, 2007 · Abstract. In this paper, we study congruence properties of coefficient of Jacobi forms. The result for elliptic modular form case was studied by Sturm (Lecture Notes in Mathematics, Springer ... intensive outpatient treatment+strategiesWebSep 14, 2013 · 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 … intensive pedagogical training instituteWebJacobi forms can be viewed as vector valued modular forms which take values in so-called Weil representations. Accordingly, the first two chapters develop the theory of finite … intensive phototherapy คือWebAug 1, 2024 · Background on Jacobi forms2.1. Jacobi forms. We first require the definition of Jacobi forms, whose theory was laid out by Eichler–Zagier [17]. A holomorphic Jacobi form of weight κ and index m on SL 2 (Z) is a holomorphic function φ: C × H → C (H is the complex upper half-plane) which satisfies the following conditions. (i) intensive outpatient rehab memphisWebMay 1, 2009 · We show that some q-series such as universal mock theta functions are linear sums of theta quotients and mock Jacobi forms of weight 1/2, which become holomorphic parts of real analytic modular forms when they are restricted to torsion points and multiplied by suitable powers of q.We also prove that certain linear sums of q-series are weakly … intensive outpatient program in staten island