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- Title
ON THE POLYNOMIAL x<sup>d</sup> + ax + b OVER 픽<sub>q</sub> AND GAUSSIAN HYPERGEOMETRIC SERIES.
- Authors
BARMAN, RUPAM; KALITA, GAUTAM
- Abstract
For d ≥ 2, denote by Pd(x) the polynomial over 픽q given by . We explicitly find the number of solutions in 픽q of the polynomial equation Pd(x) = 0 in terms of special values of dFd-1 and d-1Fd-2 Gaussian hypergeometric series with characters of orders d and d - 1 as parameters. This solves a problem posed by K. Ono (see p. 204 in [ Web of Modularity : Arithmetic of the Coefficients of Modular Forms and q-Series, CBMS Regional Conference Series in Mathematics, No. 102 (American Mathematical Society, Providence, RI, 2004)]) on special values of n+1Fn Gaussian hypergeometric series for n > 2.
- Subjects
POLYNOMIALS; HYPERGEOMETRIC series; AMERICAN Mathematical Society; PARAMETER estimation; Q-series; MODULAR forms
- Publication
International Journal of Number Theory, 2013, Vol 9, Issue 7, p1753
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042113500553