Additive number theory and maass forms

1984 ◽  
pp. 286-309 ◽  
Author(s):  
Peter Sarnak
Keyword(s):  
Number Theory ◽  
Additive Number Theory ◽  
Maass Forms ◽  
Additive Number

Additive Number Theory

Science ◽  
1936 ◽  
Vol 84 (2176) ◽  
pp. 9-9
Author(s):  
Watson Davis
Keyword(s):  
Number Theory ◽  
Additive Number Theory ◽  
Additive Number

An asymptotic formula in additive number theory

1986 ◽  
Vol 39 (4) ◽  
pp. 257-266
Author(s):  
D. Ismoilov
Keyword(s):  
Number Theory ◽  
Asymptotic Formula ◽  
Additive Number Theory ◽  
Additive Number

scholarly journals Rectification Principles in Additive Number Theory

1998 ◽  
Vol 19 (3) ◽  
pp. 343-353 ◽  
Author(s):  
Y. F. Bilu ◽  
V. F. Lev ◽  
I. Z. Ruzsa
Keyword(s):  
Number Theory ◽  
Additive Number Theory ◽  
Additive Number

scholarly journals On a conjecture of Erdös in additive number theory

1964 ◽  
Vol 10 (1) ◽  
pp. 63-70 ◽  
Author(s):  
R. Graham
Keyword(s):  
Number Theory ◽  
Additive Number Theory ◽  
Additive Number

scholarly journals The supremum of autoconvolutions, with applications to additive number theory

2009 ◽  
Vol 53 (1) ◽  
pp. 219-235 ◽  
Author(s):  
Greg Martin ◽  
Kevin O’Bryant
Keyword(s):  
Number Theory ◽  
Additive Number Theory ◽  
Additive Number

scholarly journals Some Results on Additive Number Theory III

1979 ◽  
Vol 02 (1) ◽  
pp. 159-182 ◽  
Author(s):  
Minoru TANAKA
Keyword(s):  
Number Theory ◽  
Additive Number Theory ◽  
Additive Number

A SURVEY OF FACTORIZATION COUNTING FUNCTIONS

2005 ◽  
Vol 01 (04) ◽  
pp. 563-581 ◽  
Author(s):  
A. KNOPFMACHER ◽  
M. E. MAYS
Keyword(s):  
Number Theory ◽  
Positive Integer ◽  
Additive Number Theory ◽  
Recursive Algorithms ◽  
Additive Number ◽  
Combinatorial Objects ◽  
Survey Techniques ◽  
Counting Functions ◽  
General Field ◽  
Positive Integers

The general field of additive number theory considers questions concerning representations of a given positive integer n as a sum of other integers. In particular, partitions treat the sums as unordered combinatorial objects, and compositions treat the sums as ordered. Sometimes the sums are restricted, so that, for example, the summands are distinct, or relatively prime, or all congruent to ±1 modulo 5. In this paper we review work on analogous problems concerning representations of n as a product of positive integers. We survey techniques for enumerating product representations both in the unrestricted case and in the case when the factors are required to be distinct, and both when the product representations are considered as ordered objects and when they are unordered. We offer some new identities and observations for these and related counting functions and derive some new recursive algorithms to generate lists of factorizations with restrictions of various types.

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