Generalized Theta Series and Spherical Designs

2013 ◽  
pp. 21-29
Author(s):  
Juan Cerviño ◽  
Georg Hein
Keyword(s):  
Theta Series ◽  
Spherical Designs ◽  
Generalized Theta Series

scholarly journals Weil type representations and automorphic forms

1980 ◽  
Vol 77 ◽  
pp. 145-166 ◽  
Author(s):  
Toshiaki Suzuki
Keyword(s):  
Dirichlet Series ◽  
Functional Equations ◽  
Theta Series ◽  
Type Representation ◽  
Generalized Poisson ◽  
Summation Formulae ◽  
Reciprocity Law ◽  
Weil Type ◽  
Generalized Theta Series ◽  
Poisson Summation

During 1934-1936, W. L. Ferrar investigated the relation between summation formulae and Dirichlet series with functional equations, inspired by Voronoi’s works (1904) on summation formula with respect to the numbers of divisors. In [11] A. Weil showed that the automorphic properties of theta series are expressed by generalized Poisson summation formulae with respect to the so-called Weil representation. On the other hand, T. Kubota, in his study of the reciprocity law in a number field, defined a generalized theta series and a generalized Weil type representation of SL(2, C) and obtained similar results to those of A. Weil (1970-1976, [5], [6], [7]). The methods, used by W. L. Ferrar and T. Kubota, to obtain (generalized Poisson) summation formulae depend similarly on functional equations of Dirichlet series (attached to the generalized theta series).

On the space of generalized theta-series for certain quadratic forms in any number of variables

2019 ◽  
Vol 69 (1) ◽  
pp. 87-98
Author(s):  
Ketevan Shavgulidze
Keyword(s):  
Upper Bound ◽  
Quadratic Forms ◽  
Theta Series ◽  
Vector Spaces ◽  
Generalized Theta Series

Abstract An upper bound of the dimension of vector spaces of generalized theta-series corresponding to some nondiagonal quadratic forms in any number of variables is established. In a number of cases, an upper bound of the dimension of the space of theta-series with respect to the quadratic forms of five variables is improved and the basis of this space is constructed.

scholarly journals On generalized theta series liftings

1997 ◽  
Vol 62 (2) ◽  
pp. 229-238
Author(s):  
Min Ho Lee
Keyword(s):  
Automorphic Forms ◽  
Abelian Varieties ◽  
Theta Series ◽  
Symplectic Groups ◽  
Reductive Groups ◽  
Generalized Theta Series

AbstractWe generalize dual reductive pairs by using reductive groups that are not necessarily subgroups of symplectic groups and construct the corresponding theta-series liftings for certain types of automorphic forms. We also discuss connections of such generalized theta-series liftings with families of abelian varieties parametrized by an arithmetic variety.

scholarly journals SHELLS OF SELFDUAL LATTICES VIEWED AS SPHERICAL DESIGNS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1085-1127 ◽  
Author(s):  
CLAUDE PACHE
Keyword(s):  
Modular Forms ◽  
Theta Series ◽  
Spherical Designs

We find out for which t shells of selfdual lattices and of their shadows are spherical t-designs. The method uses theta series of lattices, which are modular forms. We analyze fully cubic and Witt lattices, as well as all selfdual lattices of rank at most 24.

On the Dimension of Some Spaces of Generalized Ternary Theta-Series

2002 ◽  
Vol 9 (1) ◽  
pp. 167-178
Author(s):  
K. Shavgulidze
Keyword(s):  
Upper Bound ◽  
Quadratic Forms ◽  
Theta Series ◽  
Vector Spaces ◽  
Ternary Quadratic Forms ◽  
Generalized Theta Series

Abstract The upper bound of dimension of vector spaces of generalized theta-series corresponding to some ternary quadratic forms is established. In a number of cases, the dimension of vector spaces of generalized theta-series is established and bases of these spaces are constructed.

scholarly journals Improve concentration of frequency and time (ConceFT) by novel complex spherical designs

2021 ◽  
Vol 54 ◽  
pp. 137-144
Author(s):  
Matt Sourisseau ◽  
Yu Guang Wang ◽  
Robert S. Womersley ◽  
Hau-Tieng Wu ◽  
Wei-Hsuan Yu
Keyword(s):  
Spherical Designs ◽  
Novel Complex
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