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- W2095805724 abstract "We consider a function U = e-f0 ny,, f,' on a real affine space, here fo, .., fP are linear functions, or, . . . . ap complex numbers. The zeros of the functions fr, . . . . fP form an arrangement of hyperplanes in the affine space. We study the period matrix of the hypergeometric integrals associated with the arrangement and the function U and compute its de- terminant as an alternating product of gamma functions and critical points of the functions fo, .., fp with respect to the arrangement. In the sim- plest example, p = 1, fe = fl = t, the determinant formula takes the form so00 e -' taPi dt = r(a). We also give a determinant formula for Selberg type exponential integrals. In this case the arrangements of hyperplanes is spe- cial and admits a symmetry group, the period matrix is decomposed into blocks corresponding to different representations of the symmetry group on the space of the hypergeometric integrals associated with the arrangement. We compute the determinant of the block corresponding to the trivial rep- resentation." @default.
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- W2095805724 date "1998-01-01" @default.
- W2095805724 modified "2023-09-28" @default.
- W2095805724 title "THE DETERMINANT OF A HYPERGEOMETRIC PERIOD MATRIX" @default.
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