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.

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 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).

TOTALLY GEODESIC SURFACES AND QUADRATIC FORMS

2013 ◽  
Vol 22 (13) ◽  
pp. 1350072
Author(s):  
PRADTHANA JAIPONG
Keyword(s):  
Upper Bound ◽  
Quadratic Forms ◽  
Incompressible Surface ◽  
Totally Geodesic ◽  
Geodesic Surfaces ◽  
Figure Eight Knot ◽  
Dehn Fillings

Let M be a compact, connected, irreducible, orientable 3-manifold with torus boundary. A closed, orientable, immersed, incompressible surface F in M with no incompressible annulus joining F and ∂M compresses in at most finitely many Dehn fillings M(α). It is known that there is no universal upper bound on the number of such fillings, independent of the surface, and the figure-eight knot complement is the first example of a manifold where this phenomenon occurs. In this paper, we show that the same behavior of the figure-eight knot complement is shared by other two cusped manifolds.

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