scholarly journals Preventing SPA/DPA in ECC Systems Using the Jacobi Form

2001 ◽  
pp. 391-401 ◽  
Author(s):  
P. -Y. Liardet ◽  
N. P. Smart
Keyword(s):  
Jacobi Form

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.

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).

A geometrical approach to the Hamilton-Jacobi form of dynamics and its generalizations

1990 ◽  
Vol 13 (8) ◽  
pp. 1-74 ◽  
Author(s):  
G. Marmo ◽  
G. Morandi ◽  
N. Mukunda
Keyword(s):  
Jacobi Form ◽  
Geometrical Approach

scholarly journals A Jacobi theta series and its transformation laws

2014 ◽  
Vol 10 (06) ◽  
pp. 1343-1354
Author(s):  
Matthew Krauel
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Theta Series ◽  
Jacobi Form ◽  
Vertex Operator Algebras ◽  
Jacobi Forms ◽  
Jacobi Group

We consider a generalization of Jacobi theta series and show that every such function is a quasi-Jacobi form. Under certain conditions we establish transformation laws for these functions with respect to the Jacobi group and prove such functions are Jacobi forms. In establishing these results, we construct other functions which are also Jacobi forms. These results are motivated by applications in the theory of vertex operator algebras.

scholarly journals On the Fourier coefficients of meromorphic Jacobi forms

2014 ◽  
Vol 10 (06) ◽  
pp. 1519-1540 ◽  
Author(s):  
René Olivetto
Keyword(s):  
Analytic Functions ◽  
Fourier Coefficients ◽  
Jacobi Form ◽  
Jacobi Forms ◽  
Precise Description ◽  
Maass Forms ◽  
Real Analytic Functions ◽  
Harmonic Maass Forms ◽  
Real Analytic ◽  
Vector Valued

In this paper, we describe the automorphic properties of the Fourier coefficients of meromorphic Jacobi forms. Extending results of Dabholkar, Murthy, and Zagier, and Bringmann and Folsom, we prove that the canonical Fourier coefficients of a meromorphic Jacobi form φ(z; τ) are the holomorphic parts of some (vector-valued) almost harmonic Maass forms. We also give a precise description of their completions, which turn out to be uniquely determined by the Laurent coefficients of φ at each pole, as well as some well-known real analytic functions, that appear for instance in the completion of Appell–Lerch sums.

scholarly journals HEISENBERG AND MODULAR INVARIANCE OF N=2 CONFORMAL FIELD THEORY

2000 ◽  
Vol 15 (19) ◽  
pp. 3065-3094
Author(s):  
SHI-SHYR ROAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Theta Function ◽  
Central Charge ◽  
Jacobi Form ◽  
Modular Invariance ◽  
Function Representation ◽  
Superconformal Field Theory ◽  
Conformal Field ◽  
Modular Transformations

We present a theta function representation of the twisted characters for the rational N=2 superconformal field theory, and discuss the Jacobi-form like functional properties of these characters for a fixed central charge under the action of a finite Heisenberg group and modular transformations.

scholarly journals On the Fourier expansions of Jacobi forms

2004 ◽  
Vol 2004 (48) ◽  
pp. 2583-2594 ◽  
Author(s):  
Howard Skogman
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Jacobi Form ◽  
The Other ◽  
Jacobi Forms ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Fourier Expansions ◽  
The Relationship ◽  
Vector Valued

We use the relationship between Jacobi forms and vector-valued modular forms to study the Fourier expansions of Jacobi forms of indexesp,p2, andpqfor distinct odd primesp,q. Specifically, we show that for such indexes, a Jacobi form is uniquely determined by one of the associated components of the vector-valued modular form. However, in the case of indexes of the formpqorp2, there are restrictions on which of the components will uniquely determine the form. Moreover, for indexes of the formp, this note gives an explicit reconstruction of the entire Jacobi form from a single associated vector-valued modular form component. That is, we show how to start with a single associated vector component and use specific matrices fromSl2(ℤ)to find the other components and hence the entire Jacobi form. These results are used to discuss the possible modular forms of half-integral weight associated to the Jacobi form for different subgroups.

scholarly journals The Jacobi form D_L, theta functions, and Eisenstein series

2016 ◽  
Vol 28 (1) ◽  
pp. 75-88
Author(s):  
Abdelmejid Bayad ◽  
Gilles Robert
Keyword(s):  
Eisenstein Series ◽  
Theta Functions ◽  
Jacobi Form
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