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Building Three-Variable Homogeneous Integer-Valued Polynomials Using Generalized Projective Planes

In: Algebraic, Number Theoretic, and Topological Aspects of Ring Theory

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  • Marie MacDonald

    (Cornell University, Department of Mathematics)

Abstract

This work will present a method for constructing homogeneous integer-valued polynomials f∕pk with f ∈ ℤ [ x , y , z ] $$f\in \mathbb {Z}[x,y,z]$$ a product products of linear factors, with p a prime and k large relative to the degree of f. This is accomplished by connecting this problem to the older geometric problem of finding coverings of generalized projective planes by families of lines.

Suggested Citation

  • Marie MacDonald, 2023. "Building Three-Variable Homogeneous Integer-Valued Polynomials Using Generalized Projective Planes," Springer Books, in: Jean-Luc Chabert & Marco Fontana & Sophie Frisch & Sarah Glaz & Keith Johnson (ed.), Algebraic, Number Theoretic, and Topological Aspects of Ring Theory, pages 343-350, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-28847-0_18
    DOI: 10.1007/978-3-031-28847-0_18
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