Circle problem and the spectrum of the Laplace operator on closed 2-manifolds

Autor:	Dmitrii Aleksandrovich Popov
Rok vydání:	2019
Předmět:	Algebra Thesaurus (information retrieval) General Mathematics Spectrum (functional analysis) Laplace operator Mathematics
Zdroj:	Russian Mathematical Surveys. 74:909-925
ISSN:	1468-4829 0036-0279
DOI:	10.1070/rm9911
Popis:	In this survey the circle problem is treated in the broad sense, as the problem of the asymptotic properties of the quantity , the remainder term in the circle problem. A survey of recent results in this direction is presented. The main focus is on the behaviour of on short intervals. Several conjectures on the local behaviour of which lead to a solution of the circle problem are presented. A strong universality conjecture is stated which links the behaviour of with the behaviour of the second term in Weyl’s formula for the Laplace operator on a closed Riemannian 2-manifold with integrable geodesic flow. Bibliography: 43 titles.
Databáze:	OpenAIRE
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