CONGRUENCES CONCERNING LEGENDRE POLYNOMIALS III

DOI10.1142/S1793042113500097zbMath1277.11003arXiv1012.4234OpenAlexW2139785067MaRDI QIDQ4923261

Zhi-Hong Sun

Publication date: 6 June 2013

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

Full work available at URL: https://arxiv.org/abs/1012.4234

zbMATH Keywords

binary quadratic formLegendre polynomialcongruence

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Sums of squares and representations by other particular quadratic forms (11E25) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Congruences; primitive roots; residue systems (11A07)

Related Items (3)

Supercongruences and truncated hypergeometric series ⋮ Supercongruences on truncated hypergeometric series ⋮ On the number of representations of n as a linear combination of four triangular numbers II

Cites Work

• Unnamed Item
• Evaluation of a cubic character sum using the \(\sqrt{-19}\) division points of the curve \(y^ 2=x^ 3-2^ 3\cdot 19x+2\cdot 19^ 2\)
• Elliptic curves with complex multiplication and a character sum
• Coverings of elliptic curves with complex multiplication by hyperelliptic curves and character sums
• On character sums related to elliptic curves with complex multiplication
• Congruences involving \({2k\choose k}^2{3k\choose k}\)
• Congruences concerning Legendre polynomials. II
• On the quadratic character of quadratic units
• New cases of irreducibility for Legendre polynomials
• The Diophantine equationy²= x(x²+ 21Dx+ 112D²)and the conjectures of Birch and Swinnerton-Dyer

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