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PARITY OF THE PARTITION FUNCTION IN ARITHMETIC PROGRESSIONS, II

Published online by Cambridge University Press:  23 October 2001

MATTHEW BOYLAN  and
KEN ONO
MATTHEW BOYLAN
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, USA; boylan@math.wisc.edu, ono@math.wisc.edu
KEN ONO
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, USA; boylan@math.wisc.edu, ono@math.wisc.edu
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Abstract

Let p(n) denote the ordinary partition function. Subbarao conjectured that in every arithmetic progression r (mod t) there are infinitely many integers N ≡ r (mod t) for which p(N) is even, and infinitely many integers M ≡ r (mod t) for which p(M) is odd. We prove the conjecture for every arithmetic progression whose modulus is a power of 2.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 5 , September 2001 , pp. 558 - 564
Copyright
© The London Mathematical Society 2001

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