Real solutions of PIII(0, 0, 4, −4) on ℝ> 0

Martin Guest; Claus Hertling

doi:10.1007/978-3-319-66526-9_18

Real solutions of P_III(0, 0, 4, −4) on ℝ_{> 0}

Martin Guest^*, Claus Hertling

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

The real solutions (possibly with zeros and/or poles) of P_III(0, 0, 4, −4) on ℝ_{> 0} are by (15.10) the functions f_mult(.,s,B)|_{ℝ_>0} for (s, B) ∈ V^mat,ℝ. In this chapter we shall obtain complete results about the sequences of zeros and/or poles of these solutions. These global results will be derived by combining, first, the local behaviour for small x and for large x, and second, the geometry of the spaces M_3FN,ℝ ^mon and M_3FN,ℝ ⁱⁿⁱ=M_3FN,ℝ ^reg∪M_3FN,ℝ ^sing, which was described in Lemma 15.4 (a) and Theorem 15.5 (a).

Original language	English
Title of host publication	Lecture Notes in Mathematics
Publisher	Springer Verlag
Pages	181-196
Number of pages	16
Volume	2198
DOIs	https://doi.org/10.1007/978-3-319-66526-9_18
Publication status	Published - 2017

Publication series

Name	Lecture Notes in Mathematics
Volume	2198
ISSN (Print)	0075-8434

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1007/978-3-319-66526-9_18

Cite this

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abstract = "The real solutions (possibly with zeros and/or poles) of PIII(0, 0, 4, −4) on ℝ> 0 are by (15.10) the functions fmult(.,s,B)|ℝ>0 for (s, B) ∈ Vmat,ℝ. In this chapter we shall obtain complete results about the sequences of zeros and/or poles of these solutions. These global results will be derived by combining, first, the local behaviour for small x and for large x, and second, the geometry of the spaces M3FN,ℝ mon and M3FN,ℝ ini=M3FN,ℝ reg∪M3FN,ℝ sing, which was described in Lemma 15.4 (a) and Theorem 15.5 (a).",

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