期刊
EUROPEAN JOURNAL OF MATHEMATICS
卷 5, 期 3, 页码 909-928出版社
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s40879-018-0218-0
关键词
Tropical geometry; Summation; SL(2, Z); pi
类别
资金
- National Research University Higher School of Economics
- Young Russian Mathematics award
- ISTFELLOW program
Let f (a, b, c, d) In other words, we consider the sum of the powers of the triangle inequality defects for the lattice parallelograms (in the first quadrant) of area one. We prove that F(s) converges when s > 1 and diverges at s = 1/2. We also prove that and show a general method to obtain such formulae. The method comes from the consideration of the tropical analogue of the caustic curves, whose moduli give a complete set of continuous invariants on the space of convex domains.
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