"abstract analytic number theory" meaning in English

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          "text": "The prime number theorem serves as a prototypical example of an idea generalised via abstract analytic number theory and adapted to other fields; the emphasis is on results pertaining to asymptotic analysis.",
          "type": "example"
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        {
          "text": "1975, John Knopfmacher (editor), Abstract Analytic Number Theory, North-Holland https://books.google.com.au/books?id=HIusKnF2kmEC&printsec=frontcover&dq=%22abstract+analytic+number+theory%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjdm__u-5rsAhURIDQIHS14AjsQ6AEwAHoECAYQAg#v=onepage&q=%22abstract%20analytic%20number%20theory%22&f=false."
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          "ref": "2006, Alfred Geroldinger, Franz Halter-Koch, “Non-unique factorizations: a survey”, in James W. Brewer, Sarah Glaz, William Heinzer, Bruce Olberding, editors, Multiplicative Ideal Theory in Commutative Algebra, Springer, page 207",
          "text": "Only recently the authors completed the monograph [16] which contains a thorough presentation of the algebraic, combinatorial and analytic aspects of the theory of non-unique factorizations, together with self-contained introductions to additive group theory, to the theory of v-ideals and to abstract analytic number theory.",
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          "ref": "2006, R. Sivaramakrishnan, Certain Number-Theoretic Episodes In Algebra, Taylor & Francis (Chapman & Hall/CRC), page 339",
          "text": "In [11], J. Knopfmacher gives an interesting exposition of abstract analytic number theory wherein many of the results of classical number theory are generalized in a suitable context of semigroups satisfying certain axioms.",
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        "A branch of number theory in which suitable ideas and techniques from analytic number theory are generalised and applied to a variety of mathematical fields."
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        "(number theory) A branch of number theory in which suitable ideas and techniques from analytic number theory are generalised and applied to a variety of mathematical fields."
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          "text": "The prime number theorem serves as a prototypical example of an idea generalised via abstract analytic number theory and adapted to other fields; the emphasis is on results pertaining to asymptotic analysis.",
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          "text": "1975, John Knopfmacher (editor), Abstract Analytic Number Theory, North-Holland https://books.google.com.au/books?id=HIusKnF2kmEC&printsec=frontcover&dq=%22abstract+analytic+number+theory%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjdm__u-5rsAhURIDQIHS14AjsQ6AEwAHoECAYQAg#v=onepage&q=%22abstract%20analytic%20number%20theory%22&f=false."
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          "ref": "2006, Alfred Geroldinger, Franz Halter-Koch, “Non-unique factorizations: a survey”, in James W. Brewer, Sarah Glaz, William Heinzer, Bruce Olberding, editors, Multiplicative Ideal Theory in Commutative Algebra, Springer, page 207",
          "text": "Only recently the authors completed the monograph [16] which contains a thorough presentation of the algebraic, combinatorial and analytic aspects of the theory of non-unique factorizations, together with self-contained introductions to additive group theory, to the theory of v-ideals and to abstract analytic number theory.",
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          "text": "In [11], J. Knopfmacher gives an interesting exposition of abstract analytic number theory wherein many of the results of classical number theory are generalized in a suitable context of semigroups satisfying certain axioms.",
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        "(number theory) A branch of number theory in which suitable ideas and techniques from analytic number theory are generalised and applied to a variety of mathematical fields."
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