Well-poised hypersurfaces
نویسندگان
چکیده
An ideal I is said to be” well-poised” if all of the initial ideals obtained from points in tropical variety Trop ( ) are prime. This condition was first defined by Nathan Ilten and third...
منابع مشابه
Well-poised Generation of Apéry-like Recursions
where the fixed (but not necessarily real) parameter α satisfies the condition Reα < 1. Substituting α = 0 into the resulting recurrence equations produces the famous recursions for ζ(2) = 2Z 2 (0), ζ(3) = Z3(0) due to Apéry [Ap], as well as the recursion for ζ(4) = Z4(0) known as the Cohen–Rhin–Sorokin–Zudilin recursion ([Co], [So], [Zu1]) that is honest from both historical and alphabetical p...
متن کاملOrthogonality of Very Well-poised Series
Rodrigues formulas for very well-poised basic hypergeometric series of any order are given. Orthogonality relations are found for rational functions which generalize Rahman’s 10φ9 biorthogonal rational functions. A pair of orthogonal rational functions of type RII is identified. Elliptic analogues of some of these results are also included.
متن کاملWell-poised Hypergeometric Transformations of Euler-type Multiple Integrals
Several new multiple-integral representations are proved for well-poised hypergeometric series and integrals. The results yield, in particular, transformations of the multiple integrals that cannot be achieved by evident changes of variable. All this generalizes some classical results of Whipple and Bailey in analysis and, on the other hand, certain analytic constructions with known connection ...
متن کاملSome Remarks on Very - Well - Poised 8 φ 7 Series
Nonpolynomial basic hypergeometric eigenfunctions of the Askey–Wilson second order difference operator are known to be expressible as very-well-poised 8φ7 series. In this paper we use this fact to derive various basic hypergeometric and theta function identities. We relate most of them to identities from the existing literature on basic hypergeometric series. This leads for example to a new der...
متن کاملWell-poised Hypergeometric Service for Diophantine Problems of Zeta Values
It is explained how the classical concept of well-poised hypergeometric series and integrals becomes crucial in studing arithmetic properties of the values of Riemann’s zeta function. By these well-poised means we obtain: (1) a permutation group for linear forms in 1 and ζ(4) = π/90 yielding a conditional upper bound for the irrationality measure of ζ(4); (2) a second-order Apéry-like recursion...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2021
ISSN: ['1532-4125', '0092-7872']
DOI: https://doi.org/10.1080/00927872.2021.1879828