New theorems on the parity of partition functions

Bruce C. Berndt, Ae Ja Yee, Alexandru Zaharescu

Type: Article

Publication Date: 2004-01-05

Citations: 13

DOI: https://doi.org/10.1515/crll.2004.008

Abstract

Working in the ring A of formal power series in one variable over the field of two elements, we have recently established lower bounds for both the number of even values and the number of odd values for a wide variety of partition functions. Here, we introduce two further ideas, differential equations in A and finite perturbations, to prove theorems on the parity of a considerably larger class of partition functions.

Locations

CiteSeer X (The Pennsylvania State University) - View - PDF
Journal für die reine und angewandte Mathematik (Crelles Journal) - View

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Works Cited by This (13)

Action	Title	Year	Authors
+ PDF Chat	On the parity of partition functions	1995	Jean-Louis Nicolas Andràs Sárközy
+	Multiplicative Number Theory	1980	H. Davenport
+ PDF Chat	Periodicity modulo 𝑚 and divisibility properties of the partition function	1960	Morris Newman
+	The partition function in arithmetic progressions	1998	Ken Ono
+	Distribution of parity of the partition function in arithmetic progressions	1999	Scott Ahlgren
+	Some Remarks on the Partition Function	1966	M. V. Subbarao
+	The distribution of values of the partition function in residue classes	1983	L. Mirsky
+ PDF Chat	On the distribution of parity in the partition function	1967	T. R. Parkin Daniel Shanks
+	On the Parity of Additive Representation Functions	1998	Jean-Louis Nicolas Imre Z. Ruzsa Andràs Sárközy
+	ON THE PARITY OF PARTITION FUNCTIONS	2003	Bruce C. Berndt Ae Ja Yee Alexandru Zaharescu