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Preliminaries

In: Representations of Integers as Sums of Squares

Author

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  • Emil Grosswald

    (Temple University, College of Liberal Arts)

Abstract

In this book, when we speak of a quadratic form,* we mean a rational, integral quadratic form, unless the contrary is stated explicitly. Given a quadratic form Q, let N Q be the set of values of Q where x ∈ ℤ k (i.e., x i ∈ ℤ for i = 1, 2, ..., k); clearly, N Q ⊂ ℤ. If $$ Q = \sum\nolimits_{i = 1}^k {x_i^2} $$ , we denote N Q by N k . The main problems that we shall study can now be formulated as follows: (a) Given a quadratic form Q, determine N Q . (b) Given Q and n ∈ N Q , determine the number of representations of n by Q, i.e., the number of vectors x ∈ ℤk for which Q(x) = n.

Suggested Citation

  • Emil Grosswald, 1985. "Preliminaries," Springer Books, in: Representations of Integers as Sums of Squares, chapter 0, pages 5-12, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8566-0_2
    DOI: 10.1007/978-1-4613-8566-0_2
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