On the location of the zero-free half-plane of a random Epstein zeta function
| Autor: | Andreas Strömbergsson, Anders Södergren |
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| Rok vydání: | 2017 |
| Předmět: |
Mathematics - Number Theory
Plane (geometry) Limit distribution General Mathematics Probability (math.PR) 010102 general mathematics Dimension (graph theory) Zero (complex analysis) 01 natural sciences Infimum and supremum Riemann zeta function Combinatorics symbols.namesake Distribution function 11M41 (Primary) 11E45 60G55 (Secondary) 0103 physical sciences FOS: Mathematics symbols Number Theory (math.NT) 010307 mathematical physics 0101 mathematics Random variable Mathematics - Probability Mathematics |
| Zdroj: | Mathematische Annalen. 371:1191-1227 |
| ISSN: | 1432-1807 0025-5831 |
| Popis: | In this note we study, for a random lattice L of large dimension n, the supremum of the real parts of the zeros of the Epstein zeta function E_n(L,s) and prove that this random variable has a limit distribution, which we give explicitly. This limit distribution is studied in some detail; in particular we give an explicit formula for its distribution function. Comment: To appear in Mathematische Annalen. The final publication is available at https://link.springer.com/article/10.1007/s00208-017-1589-0 |
| Databáze: | OpenAIRE |
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