On the uniqueness of minimal definitizing polynomials for a sequence with finitely many negative squares

1988 ◽  
pp. 93-99 ◽  
Author(s):  
Christian Berg
Keyword(s):  
Negative Squares

scholarly journals Sequences with finitely many negative squares

1988 ◽  
Vol 79 (2) ◽  
pp. 260-287 ◽  
Author(s):  
C Berg ◽  
J.P.R Christensen ◽  
P.H Maserick
Keyword(s):  
Negative Squares

AUTOMORPHIC FORMS AND LORENTZIAN KAC–MOODY ALGEBRAS PART I

1998 ◽  
Vol 09 (02) ◽  
pp. 153-199 ◽  
Author(s):  
VALERI A. GRITSENKO ◽  
VIACHESLAV V. NIKULIN
Keyword(s):  
Mirror Symmetry ◽  
Automorphic Forms ◽  
Parabolic Type ◽  
Elliptic Type ◽  
Reflection Groups ◽  
Type Iv ◽  
Homogeneous Domains ◽  
Negative Squares ◽  
Cartan Matrices ◽  
General Method

Using the general method which was applied to prove finiteness of the set of hyperbolic generalized Cartan matrices of elliptic and parabolic type, we classify all symmetric (and twisted to symmetric) hyperbolic generalized Cartan matrices of elliptic type and of rank 3 with a lattice Weyl vector. We develop the general theory of reflective lattices T with 2 negative squares and reflective automorphic forms on homogeneous domains of type IV defined by T. We consider this theory as mirror symmetric to the theory of elliptic and parabolic hyperbolic reflection groups and corresponding hyperbolic root systems. We formulate Arithmetic Mirror Symmetry Conjecture relating both these theories and prove some statements to support this Conjecture. This subject is connected with automorphic correction of Lorentzian Kac–Moody algebras. We define Lie reflective automorphic forms which are the most beautiful automorphic forms defining automorphic Lorentzian Kac–Moody algebras and formulate finiteness Conjecture for these forms. Detailed study of automorphic correction and Lie reflective automorphic forms for generalized Cartan matrices mentioned above will be given in Part II.

XXIII.—Representations of a Number as the Sum of a Large Number of Squares

1961 ◽  
Vol 65 (4) ◽  
pp. 318-331 ◽  
Author(s):  
R. A Rankin
Keyword(s):  
Asymptotic Formula ◽  
Negative Squares

SYNOPSISAn asymptotic formula is given for the number r(s, P; N) of representations of an integer N as the sum of s non-negative squares, where each square does not exceed P2. The numbers s, P and N are large and are subject to certain conditions, one of which is that N is approximately ⅓sP2.

scholarly journals On the negative squares of a class of self-adjoint extensions in Krein spaces

2013 ◽  
Vol 286 (2-3) ◽  
pp. 118-148 ◽  
Author(s):  
Jussi Behrndt ◽  
Annemarie Luger ◽  
Carsten Trunk
Keyword(s):  
Krein Spaces ◽  
Negative Squares

scholarly journals On elements with negative squares

1972 ◽  
Vol 31 (1) ◽  
pp. 57-57 ◽  
Author(s):  
Ralph DeMarr ◽  
Arthur Steger
Keyword(s):  
Negative Squares
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