ON THE POLYNOMIAL xd + ax + b OVER 𝔽q AND GAUSSIAN HYPERGEOMETRIC SERIES

DOI10.1142/S1793042113500553zbMath1306.11050MaRDI QIDQ2866998

Gautam Kalita, Rupam Barman

Publication date: 10 December 2013

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

Gaussian hypergeometric seriespolynomial equationcharacters of finite fields

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Polynomials over finite fields (11T06) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (7)

Hypergeometric functions and algebraic curves $y^e=x^d+ax+b$ ⋮ Unnamed Item ⋮ Certain character sums, Gaussian hypergeometric series, and their connections to algebraic curves ⋮ Number of complete subgraphs of peisert graphs and finite field hypergeometric functions ⋮ Hyperelliptic curves and values of Gaussian hypergeometric series ⋮ On the polynomials \(x^d+ax^i+b\) and \(x^d+ax^{d-i}+b\) over \(\mathbb F_q\) and Gaussian hypergeometric series ⋮ \(p\)-adic gamma function and the polynomials \(x^d + ax + b\) and \(x^d + ax^{d-1} + b\) over \(\mathbb{F}_q\)

Cites Work

• Hypergeometric functions and a family of algebraic curves
• Trace formulas for Hecke operators, Gaussian hypergeometric functions, and the modularity of a threefold
• Elliptic curves and special values of Gaussian hypergeometric series
• CERTAIN VALUES OF GAUSSIAN HYPERGEOMETRIC SERIES AND A FAMILY OF ALGEBRAIC CURVES
• Gaussian hypergeometric evaluations of traces of Frobenius for elliptic curves
• HYPERGEOMETRIC FUNCTIONS OVER FINITE FIELDS AND THEIR RELATIONS TO ALGEBRAIC CURVES
• Hypergeometric functions over ${\mathbb {F}_p}$ and relations to elliptic curves and modular forms
• Values of Gaussian hypergeometric series
• A Gaussian hypergeometric series evaluation and Apéry number congruences
• Unnamed Item

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