scholarly journals Flat structure for the simple elliptic singularity of type $\tilde E_6$ and Jacobi form

1993 ◽  
Vol 69 (7) ◽  
pp. 247-251 ◽  
Author(s):  
Ikuo Satake
Keyword(s):  
Jacobi Form ◽  
Flat Structure ◽  
Elliptic Singularity

scholarly journals Higher pullbacks of modular forms on orthogonal groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Brandon Williams
Keyword(s):  
Modular Forms ◽  
Differential Operators ◽  
Jacobi Form ◽  
Siegel Modular Forms ◽  
Orthogonal Groups

Abstract We apply differential operators to modular forms on orthogonal groups O ⁢ ( 2 , ℓ ) {\mathrm{O}(2,\ell)} to construct infinite families of modular forms on special cycles. These operators generalize the quasi-pullback. The subspaces of theta lifts are preserved; in particular, the higher pullbacks of the lift of a (lattice-index) Jacobi form ϕ are theta lifts of partial development coefficients of ϕ. For certain lattices of signature ( 2 , 2 ) {(2,2)} and ( 2 , 3 ) {(2,3)} , for which there are interpretations as Hilbert–Siegel modular forms, we observe that the higher pullbacks coincide with differential operators introduced by Cohen and Ibukiyama.

Contributions to love-wave transformation theory: Earth-flattening transformation for love waves from a point source in a sphere

1973 ◽  
Vol 63 (3) ◽  
pp. 983-993
Author(s):  
Edgar Kausel ◽  
Fred Schwab
Keyword(s):  
Point Source ◽  
Love Wave ◽  
Love Waves ◽  
Wave Transformation ◽  
Transformation Theory ◽  
Flat Structure ◽  
Wave Response

abstract By means of the Biswas-Knopoff (1970) transformation, programs for the computation of the Love-wave response to a point source in a flat structure can be modified, quite easily, to compute the response in a sphere.

Approximate Range Querying over Sliding Windows

2009 ◽  
pp. 2037-2050
Author(s):  
Francesco Buccafurri ◽  
Gianluca Caminiti ◽  
Gianluca Lax
Keyword(s):  
Knowledge Discovery ◽  
Data Reduction ◽  
Experimental Analysis ◽  
Window Size ◽  
Sliding Window ◽  
Knowledge Discovery In Databases ◽  
Flat Structure ◽  
Sliding Windows ◽  
Reduction Techniques ◽  
Processing Step

In the context of Knowledge Discovery in Databases, data reduction is a pre-processing step delivering succinct yet meaningful data to sequent stages. If the target of mining are data streams, then it is crucial to suitably reduce them, since often analyses on such data require multiple scans. In this chapter, we propose a histogram-based approach to reducing sliding windows supporting approximate arbitrary (i.e., non biased) range-sum queries. The histogram is based on a hierarchical structure (as opposed to the flat structure of traditional ones) and it results suitable to directly support hierarchical queries, such as drill-down and roll-up operations. In particular, both sliding window shifting and quick query answering operations are logarithmic in the sliding window size. Experimental analysis shows the superiority of our method in terms of accuracy w.r.t. the state-of-the-art approaches in the context of histogram-based sliding window reduction techniques.

A Note on the Multiplicity of Cohen-Macaulay Algebras with Pure Resolutions

1985 ◽  
Vol 37 (6) ◽  
pp. 1149-1162 ◽  
Author(s):  
Craig Huneke ◽  
Matthew Miller
Keyword(s):  
Tangent Cone ◽  
Betti Numbers ◽  
Rational Surface ◽  
Minimal Resolution ◽  
Homogeneous Ideal ◽  
Elliptic Singularity ◽  
Rational Surface Singularity ◽  
Generic Matrix ◽  
Image Position ◽  
Coordinate Rings

Let R = k[X1, …, Xn] with k a field, and let I ⊂ R be a homogeneous ideal. The algebra R/I is said to have a pure resolution if its homogeneous minimal resolution has the formSome of the known examples of pure resolutions include the coordinate rings of: the tangent cone of a minimally elliptic singularity or a rational surface singularity [15], a variety defined by generic maximal Pfaffians [2], a variety defined by maximal minors of a generic matrix [3], a variety defined by the submaximal minors of a generic square matrix [6], and certain of the Segre-Veronese varieties [1].If I is in addition Cohen-Macaulay, then Herzog and Kühl have shown that the betti numbers bi are completely determined by the twists di.

scholarly journals On the Fourier expansions of Jacobi forms of half-integral weight

2006 ◽  
Vol 2006 ◽  
pp. 1-11
Author(s):  
B. Ramakrishnan ◽  
Brundaban Sahu
Keyword(s):  
Modular Forms ◽  
Jacobi Form ◽  
Jacobi Forms ◽  
Number Of Components ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Fourier Expansions ◽  
The Given ◽  
The Relationship ◽  
Vector Valued

Using the relationship between Jacobi forms of half-integral weight and vector valued modular forms, we obtain the number of components which determine the given Jacobi form of indexp,p2orpq, wherepandqare odd primes.

scholarly journals VERTEX OPERATOR ALGEBRAS AND WEAK JACOBI FORMS

2012 ◽  
Vol 23 (06) ◽  
pp. 1250024 ◽  
Author(s):  
MATTHEW KRAUEL ◽  
GEOFFREY MASON
Keyword(s):  
Vertex Operator ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Congruence Subgroup ◽  
Modular Function ◽  
Jacobi Form ◽  
Jacobi Forms ◽  
Order Automorphism ◽  
Strongly Regular ◽  
Vector Valued

Let V be a strongly regular vertex operator algebra. For a state h ∈ V1 satisfying appropriate integrality conditions, we prove that the space spanned by the trace functions Tr M qL(0)-c/24ζh(0) (M a V-module) is a vector-valued weak Jacobi form of weight 0 and a certain index 〈h, h〉/2. We discuss refinements and applications of this result when V is holomorphic, in particular we prove that if g = eh(0) is a finite-order automorphism then Tr V qL(0)-c/24g is a modular function of weight 0 on a congruence subgroup of SL 2(ℤ).

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