Matches in SemOpenAlex for { <https://semopenalex.org/work/W2810134905> ?p ?o ?g. }
Showing items 1 to 56 of
56
with 100 items per page.
- W2810134905 endingPage "207" @default.
- W2810134905 startingPage "187" @default.
- W2810134905 abstract "In this paper we consider a new class of Dirichlet series, the zeta functions of monoids of natural numbers. The inverse Dirichlet series for the zeta function of monoids of natural numbers are studied. It is shown that the existence of an Euler product for the zeta function of a monoid is related to the uniqueness of the factorization into prime factors in this monoid. The notion of coprime sets of natural numbers is introduced and it is shown that for such sets the multiplicativity of minimal monoids and corresponding zeta-functions of monoids takes place. It is shown that if all prime elements of a monoid are prime numbers, then the characteristic function of the monoid is a multiplicative function and in this case the zeta function of the monoid is a generalized L-function. Various examples of monoids and corresponding zeta functions of monoids are considered. The relation between the inversion of the zeta function of a monoid and the generalized Mo¨bius function on a monoid as a partially ordered set is studied by means of the divisibility of natural numbers. A number of properties of the zeta functions of monoids of natural numbers with a unique decomposition into prime factors are obtained. The paper deals with taking the logarithm of an Eulerian product as a function of a complex argument. It is shown that a continuous function that determines the value of the logarithm of an Euler product runs through all branches of the infinite-valued function of the logarithm near its pole. The corollaries on the value of a complex-valued function of a special form near a singular point are obtained. These properties imply statements about the values of the Riemann zeta function near the boundary of the region of absolute convergence. Using Bertrand’s postulate, infinite exponential sequences of prime numbers are introduced. It is shown that corresponding zeta-functions of monoids of natural numbers converge absolutely in the whole half-plane with a positive real part. Since such zeta-functions of monoids of natural numbers can be decomposed into an Euler product in the whole region of absolute convergence, they do not have zeros in the entire half-plane with a positive real part. In conclusion, topical problems with zeta-functions of monoids of natural numbers that require further investigation are considered." @default.
- W2810134905 created "2018-07-10" @default.
- W2810134905 creator A5007163583 @default.
- W2810134905 date "2018-03-20" @default.
- W2810134905 modified "2023-09-25" @default.
- W2810134905 title "ДЗЕТА-ФУНКЦИЯ МОНОИДОВ НАТУРАЛЬНЫХ ЧИСЕЛ С ОДНОЗНАЧНЫМ РАЗЛОЖЕНИЕМ НА ПРОСТЫЕ МНОЖИТЕЛИ1" @default.
- W2810134905 doi "https://doi.org/10.22405/2226-8383-2017-18-4-187-207" @default.
- W2810134905 hasPublicationYear "2018" @default.
- W2810134905 type Work @default.
- W2810134905 sameAs 2810134905 @default.
- W2810134905 citedByCount "0" @default.
- W2810134905 crossrefType "journal-article" @default.
- W2810134905 hasAuthorship W2810134905A5007163583 @default.
- W2810134905 hasBestOaLocation W28101349051 @default.
- W2810134905 hasConcept C112343008 @default.
- W2810134905 hasConcept C114614502 @default.
- W2810134905 hasConcept C118615104 @default.
- W2810134905 hasConcept C138888516 @default.
- W2810134905 hasConcept C149685015 @default.
- W2810134905 hasConcept C184264201 @default.
- W2810134905 hasConcept C202444582 @default.
- W2810134905 hasConcept C206901836 @default.
- W2810134905 hasConcept C33923547 @default.
- W2810134905 hasConcept C35235930 @default.
- W2810134905 hasConceptScore W2810134905C112343008 @default.
- W2810134905 hasConceptScore W2810134905C114614502 @default.
- W2810134905 hasConceptScore W2810134905C118615104 @default.
- W2810134905 hasConceptScore W2810134905C138888516 @default.
- W2810134905 hasConceptScore W2810134905C149685015 @default.
- W2810134905 hasConceptScore W2810134905C184264201 @default.
- W2810134905 hasConceptScore W2810134905C202444582 @default.
- W2810134905 hasConceptScore W2810134905C206901836 @default.
- W2810134905 hasConceptScore W2810134905C33923547 @default.
- W2810134905 hasConceptScore W2810134905C35235930 @default.
- W2810134905 hasIssue "4" @default.
- W2810134905 hasLocation W28101349051 @default.
- W2810134905 hasLocation W28101349052 @default.
- W2810134905 hasOpenAccess W2810134905 @default.
- W2810134905 hasPrimaryLocation W28101349051 @default.
- W2810134905 hasRelatedWork W1978442146 @default.
- W2810134905 hasRelatedWork W2005669171 @default.
- W2810134905 hasRelatedWork W2018682603 @default.
- W2810134905 hasRelatedWork W2024476204 @default.
- W2810134905 hasRelatedWork W2117407358 @default.
- W2810134905 hasRelatedWork W2564120157 @default.
- W2810134905 hasRelatedWork W2810134905 @default.
- W2810134905 hasRelatedWork W2910810623 @default.
- W2810134905 hasRelatedWork W3001420250 @default.
- W2810134905 hasRelatedWork W4361762021 @default.
- W2810134905 hasVolume "18" @default.
- W2810134905 isParatext "false" @default.
- W2810134905 isRetracted "false" @default.
- W2810134905 magId "2810134905" @default.
- W2810134905 workType "article" @default.