Word.ws English Dictionary

additive number theory

additive number theory noun: the subfield of number theory concerning the behaviour of sumsets (integer sets added to each other elementwise).

Noun

additive number theory (uncountable)

  1. The subfield of number theory concerning the behaviour of sumsets (integer sets added to each other elementwise).
    • Abstractly, additive number theory includes the study of abelian groups and commutative semigroups with an addition operation.
    • Two principal objects of study in additive number theory are the sumset A#43;B#61;#92;#123;a#43;b#58;a#92;inA,b#92;inB#92;#125; of two subsets A and B of elements from an abelian group G, and the h-fold sumset of A, hA#61;#92;underset#123;h#125;#123;#92;underbrace#123;A#43;#92;cdots#43;A

Examples of additive number theory in a sentence

  • Additive number theory has close ties to combinatorial number theory and the geometry of numbers.
  • The Circle Method is a beautiful idea for studying many problems in additive number theory.2006, Steven J. Miller, Ramin Takloo-Bighash, An Invitation to Modern Number Theory, Princeton University Press, page 303:
  • Additive number theory is a very broad area within which lies the theory of partitions, and the subject of representation of integers as sums of squares, cubes, etc.2008, Krishnaswami Alladi, editor, Surveys in Number Theory, Springer, page ix:

Questions about additive number theory

What does additive number theory mean?
Additive number theory means the subfield of number theory concerning the behaviour of sumsets (integer sets added to each other elementwise).
How do you use additive number theory in a sentence?
Additive number theory has close ties to combinatorial number theory and the geometry of numbers.
What part of speech is additive number theory?
Additive number theory is a noun.

Words near additive number theory in the dictionary

  1. additive identities
  2. additive identity
  3. additive inverse
  4. additive inverses
  5. additive manufacturing
  6. additive number theory
  7. additive operation
  8. additive operations
  9. additive plural
  10. additive plurals
  11. additively

Source and license

Adapted from Wiktionary: additive number theory (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

Cite this entry: “additive number theory.” Word.ws, https://word.ws/additive_number_theory. Based on Wiktionary, CC BY-SA 4.0.