A FAMILY OF -SUPERCONGRUENCES MODULO THE CUBE OF A CYCLOTOMIC POLYNOMIAL
Victor J. W. Guo, Michael J. Schlosser
Abstract
Abstract We establish a family of q -supercongruences modulo the cube of a cyclotomic polynomial for truncated basic hypergeometric series. This confirms a weaker form of a conjecture of the present authors. Our proof employs a very-well-poised Karlsson–Minton type summation due to Gasper, together with the ‘creative microscoping’ method introduced by the first author in recent joint work with Zudilin.
Topics & Concepts
MathematicsModuloCyclotomic polynomialCube (algebra)ConjectureHypergeometric functionPolynomialHypergeometric identityAlgebra over a fieldArithmeticCombinatoricsPure mathematicsDiscrete mathematicsGeneralized hypergeometric functionMathematical analysisHypergeometric function of a matrix argumentAdvanced Mathematical IdentitiesMathematical functions and polynomialsAnalytic Number Theory Research