Forms Representable by an Integral Positive-Definite Binary Quadratic Form.
نویسندگان
چکیده
منابع مشابه
Representations of integers by certain positive definite binary quadratic forms
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n= x2 +Ny2 for a squarefree integer N .
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As a generalization of the famous four square theorem of Lagrange, Ramanujan and Willerding found all positive definite integral quaternary quadratic forms that represent all positive integers. In this paper, we find all positive definite integral quinary quadratic forms that represent all positive definite integral binary quadratic forms. We also discuss recent results on positive definite int...
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The level N and squarefree character q of a positive definite ternary quadratic form are defined so that its associated modular form has level N and character Xg ■ We define ä collection of correspondences between classes of quadratic forms having the same level and different discriminants. This makes practical a method for finding representatives of all classes of ternary forms having a given ...
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In this paper, the integral binary quadratic forms for which the set of represented values is closed under k-fold products, for even positive integers k, will be characterized. This property will be seen to distinguish the elements of odd order in the form class group of a fixed discriminant. Further, it will be shown that this closure under k-fold products can always be expressed by a klinear ...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1971
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-11036