J. Aust. Math. Soc.
81 (2006), 21-34
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Finite Fourier series and ovals in PG
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Bernhard Schmidt
School of Physical and Mathematical Sciences
Nanyang Technological University
No. 1 Nanyang Walk, Blk 5, Level 3
Singapore 637616
bernhard@ntu.edu.sg
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Abstract
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We propose the use of finite Fourier series as
an alternative means of representing ovals in
projective planes of even order. As an example
to illustrate the method's potential, we show
that the set
forms an oval if
is a primitive
root of unity in
and
is viewed as an affine plane over
. For the verification, we only need some
elementary `trigonometric identities' and a basic
irreducibility lemma that is of independent
interest. Finally, we show that our example is
the Payne oval when
is odd, and the Adelaide oval when
is even.
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Australian Mathematical Publishing Association Inc.
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©
Australian MS
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