On the order map for hypersurface coamoebas

Forsgård, Jens; Johansson, Petter

doi:10.48550/arxiv.1205.2014

Cited by 4 publications

(17 citation statements)

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“…where b i denotes the ith row of the matrix B. For connections between camoebas and Gale duals, see [NP10,FJ12].…”

Section: Lopsided Coamebas and Mellin-barnes Integralsmentioning

confidence: 99%

“…There are several ways to define the lopsided coamoeba; for a more exhaustive treatment, we refer the reader to [FJ12]. The name "lopsided coamoeba" can be misleading; the lopsided coamoeba is not a actually a coamoeba itself, but it can be viewed as a crude approximation of the coamoeba.…”

Section: Lopsided Coamebas and Mellin-barnes Integralsmentioning

confidence: 99%

“…Remark 5.3. The main result of [FJ12] states that the set of connected components of the complement of LA f is equipped with an order map. Fix α = (α 1 , .…”

Section: Lopsided Coamebas and Mellin-barnes Integralsmentioning

confidence: 99%

“…We note that there exist matrices A whose associated coamoeba has fewer than the desired vol(A)many number of connected components in the complement of its closure for all choices of coefficients c [For12]. On the other hand, if A is a circuit, then when β is totally nonresonant, there always exists a Mellin-Barnes, and hence an extended Euler-Mellin, basis of integral representations for solutions of H A (β) [FJ12].…”

Section: A-hypergeometric Rank-jumping Examplementioning

confidence: 99%

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Euler-Mellin integrals and A-hypergeometric functions

2014

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We consider integrals that generalize both the Mellin transforms of rational functions of the form 1/f and the classical Euler integrals. The domains of integration of our so-called Euler-Mellin integrals are naturally related to the coamoeba of f , and the components of the complement of the closure of the coamoeba give rise to a family of these integrals. After performing an explicit meromorphic continuation of Euler-Mellin integrals, we interpret them as A-hypergeometric functions and discuss their linear independence and relation to Mellin-Barnes integrals.

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“…where b i denotes the ith row of the matrix B. For connections between camoebas and Gale duals, see [NP10,FJ12].…”

Section: Lopsided Coamebas and Mellin-barnes Integralsmentioning

confidence: 99%

Section: Lopsided Coamebas and Mellin-barnes Integralsmentioning

confidence: 99%

“…Remark 5.3. The main result of [FJ12] states that the set of connected components of the complement of LA f is equipped with an order map. Fix α = (α 1 , .…”

Section: Lopsided Coamebas and Mellin-barnes Integralsmentioning

confidence: 99%

Section: A-hypergeometric Rank-jumping Examplementioning

confidence: 99%

See 2 more Smart Citations