abstract analytic number theory

Definitions

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.

uncountable

Examples

“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 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.”

“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.”

CEFR level