abstract analytic number theory

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Noun

abstract analytic number theory (uncountable)

  1. (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.
    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.
    • 1975, John Knopfmacher (editor), Abstract Analytic Number Theory, North-Holland .
    • 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:
      Only recently the authors completed the monograph 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 -ideals and to abstract analytic number theory.
    • 2006, R. Sivaramakrishnan, Certain Number-Theoretic Episodes In Algebra‎, Taylor & Francis (Chapman & Hall/CRC), page 339:
      In , 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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