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A Note on Bernoulli-Goss Polynomials

Published online by Cambridge University Press:  20 November 2018

K. Ireland and
D. Small
K. Ireland
Affiliation:
Department of Mathematics and Statistics, University of New Brunswick P. O. Box 4400, Fredericton New Brunswick E3B 5 A3
D. Small
Affiliation:
Department of Mathematics and Statistics, University of New Brunswick P. O. Box 4400, Fredericton New Brunswick E3B 5 A3
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Abstract

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In an important series of papers ([3], [4], [5]), (see also Rosen and Galovich [1], [2]), D. Goss has developed the arithmetic of cyclotomic function fields. In particular, he has introduced Bernoulli polynomials and proved a non-existence theorem for an analogue to Fermat’s equation for regular “exponent”. For each odd prime p and integer n, l ≤ n ≤ p 2-2 we derive a closed form for the nth Bernoulli polynomial. Using this result a computer search for regular quadratic polynomials of the form x 2-a was made. For primes less than or equal to 269 regular quadratics exist for p= 3, 5, 7, 13, 31.

Keywords

12C15

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 2 , 01 June 1984, pp. 179 - 184
Copyright
Copyright © Canadian Mathematical Society 1984

References

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