abstract analytic number theory

noun

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.

“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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Meanings

nounabstract analytic number theory (uncountable)
  1. uncountablemathematicsA branch of number theory in which suitable ideas and techniques from analytic number theory are generalised and applied to a variety of mathematical fields.

    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.

    3 more examples

    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.

    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.

    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

    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.

    2006, R. Sivaramakrishnan, Certain Number-Theoretic Episodes In Algebra, Taylor & Francis (Chapman & Hall/CRC), page 339

Translations

Polish abstrakcyjna analityczna teoria liczb
  • abstrakcyjna analityczna teoria liczbbranch of number theory
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APA

abstract analytic number theory. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/abstract%20analytic%20number%20theory

MLA

“abstract analytic number theory.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/abstract%20analytic%20number%20theory. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “abstract analytic number theory,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/abstract%20analytic%20number%20theory.

Source: abstract analytic number theory on Wiktionary, CC BY-SA 4.0.