Geodesic
A Note on Bernoulli-Goss Polynomials
Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 179-184

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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.
DOI : 10.4153/CMB-1984-027-1
Mots-clés : 12C15 
Ireland, K.; Small, D. A Note on Bernoulli-Goss Polynomials. Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 179-184. doi: 10.4153/CMB-1984-027-1
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[1] 1. Galovich, S. and Rosen, M., The Class Number of Cyclotomic Function Fields, Journal of Number Theory, Vol. 13, No. 3, August 1981, 363–375. Google Scholar

[2] 2. Galovich, S. and Rosen, M., Unit and Class Groups in Cyclotomic Function Fields, Journal of Number Theory, Vol. 14, No. 2, 1982. Google Scholar

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[7] 7. Thomas, E., On the Zeta Function for Function Fields Over , Pacific Journal of Math., 107, (1), 1983, 251–256. Google Scholar

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