Hypergeometric template (1/4): (α, β) format
A hypergeometric template is a pair of multisets of rational numbers α = (α1, . . . , αd) and
β = (β1, . . . , βd) having the same number of elements. We set
A(x) =
Y
16j6d
(x − e2πiαj
), B(x) =
Y
16k6d
(x − e2πiβk
) .
We make the following assumptions:
αj 6≡ βk (mod 1) for all j and k; or equivalently gcd(A, B) = 1.
αj /
∈ Z for all j; or equivalently A(1) 6= 0.
our template is defined over Q, in other words A, B ∈ Z[x]; or equivalently if some a/D
with gcd(a, D) = 1 occurs in the αj or βk, then all the b/D modulo 1 with
gcd(b, D) = 1 also occur.
Atelier 2022 (13/01/2022) – p. 3/12