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تسجيل مستخدم جديدSome new $q$-congruences for truncated basic hypergeometric series
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We provide several new $q$-congruences for truncated basic hypergeometric series, mostly of arbitrary order. Our results include congruences modulo the square or the cube of a cyclotomic polynomial, and in some instances, parametric generalizations thereof. These are established by a variety of techniques including polynomial argument, creative microscoping (a method recently introduced by the first author in collaboration with Zudilin), Andrews multiseries generalization of the Watson transformation, and induction. We also give a number of related conjectures including congruences modulo the fourth power of a cyclotomic polynomial.
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We provide several new $q$-congruences for truncated basic hypergeometric series with the base being an even power of $q$. Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding on
es of an earlier paper containing $q$-congruences for truncated basic hypergeometric series with the base being an odd power of $q$. We also give a number of related conjectures including $q$-congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3.
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We prove general Dwork-type congruences for constant terms attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and $p$-adic analytic properties of functions originating from polynomial solutions modulo $p^s$ of
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