Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Partitions into Primes
HTML articles powered by AMS MathViewer

by Yifan Yang PDF
Trans. Amer. Math. Soc. 352 (2000), 2581-2600 Request permission

Abstract:

We investigate the asymptotic behavior of the partition function $p_{\Lambda } (n)$ defined by $\sum ^{\infty }_{n=0}p_{\Lambda } (n)x^{n} =\prod ^{\infty }_{m=1}(1-x^{m})^{-\Lambda (m)}$, where $\Lambda (n)$ denotes the von Mangoldt function. Improving a result of Richmond, we show that $\log p_{\Lambda } (n)=2\sqrt {\zeta (2)n}+O(\sqrt n\exp \{-c(\log n) (\log _{2} n)^{-2/3}(\log _{3} n)^{-1/3}\})$, where $c$ is a positive constant and $\log _{k}$ denotes the $k$ times iterated logarithm. We also show that the error term can be improved to $O(n^{1/4})$ if and only if the Riemann Hypothesis holds.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 11P82, 11M26, 11N05
  • Retrieve articles in all journals with MSC (2000): 11P82, 11M26, 11N05
Additional Information
  • Yifan Yang
  • Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
  • MR Author ID: 633505
  • Email: yfyang@math.uiuc.edu
  • Received by editor(s): March 3, 1998
  • Published electronically: February 14, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 2581-2600
  • MSC (2000): Primary 11P82; Secondary 11M26, 11N05
  • DOI: https://doi.org/10.1090/S0002-9947-00-02386-2
  • MathSciNet review: 1621714