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We introduce a Julia implementation of the recently proposed Nevanlinna analytic continuation method. The method is based on Nevanlinna interpolants and inherently preserves the causality of a response function due to its construction. For theoretical calculations without statistical noise, this continuation method is a powerful tool to extract real-frequency information from numerical input data on the Matsubara axis. This method has been applied to first-principles calculations of correlated materials. This paper presents its efficient and full-featured open-source implementation of the method including the Hamburger moment problem and smoothing.
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An Evertse–Ferretti Nevanlinna constant and its consequences
Abstract In this paper, we introduce the notion of an Evertse–Ferretti Nevanlinna constant and compare it with the birational Nevanlinna constant introduced by the authors in a recent joint paper. We then use it to recover several previously known results. This includes a 1999 example of Faltings from hisBaker’s Gardenarticle. We also extend the theory of these Nevanlinna constants to what we call “multidivisor Nevanlinna constants,” which allow the proximity function to involve the maximum of Weil functions for finitely many divisors.
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- Award ID(s):
- 1646385
- PAR ID:
- 10283353
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Monatshefte für Mathematik
- Volume:
- 196
- Issue:
- 2
- ISSN:
- 0026-9255
- Page Range / eLocation ID:
- p. 305-334
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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