abstract analytic number theory

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 [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 ${\displaystyle v}$-ideals and to abstract analytic number theory.

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

     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.

• Beurling zeta function on Wikipedia.Wikipedia