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PARTITIONS INTO PRIME POWERS
Author(s) -
Gafni Ayla
Publication year - 2021
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12082
Subject(s) - mathematics , partition (number theory) , combinatorics , extension (predicate logic) , prime (order theory) , asymptotic formula , set (abstract data type) , discrete mathematics , programming language , computer science
Abstract For a subset A ⊂ N , letp A ( n )denote the restricted partition function which counts partitions of n with all parts lying in A . In this paper, we use a variation of the Hardy–Littlewood circle method to provide an asymptotic formula forp A ( n ) , where A is the set of k th powers of primes (for fixed k ). This combines Vaughan's work on partitions into primes with the author's previous result about partitions into k th powers. This new asymptotic formula is an extension of a pattern indicated by several results about restricted partition functions over the past few years. Comparing these results side‐by‐side, we discuss a general strategy by which one could analyzep A ( n )for a given set A .

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