Abstract
In 2008, Lovejoy and Osburn defined the generating function for .In 2009, Byungchan Kim defined the generating function for .This paper shows how to discuss the generating functions for and . Byungchan Kim also defined with increasing relation and overpartitioncongruences mod 4,8 and 64. In 2006, Berndt found the relation has two values with certain restrictions and various formulae by the common term .This paper shows how to prove the four Theorems about overpartitions modulo 8.These Theorems satisfy the arithmetic properties of the overpartition function modulo 8.
Highlights
In this paper we give some related definitions of overpartition, ( ), Pk (n), d(n), di,[4] (n), (n) and (n)
We prove the four Theorems about overpartitions modulo 8 with certain conditions of n
Overpartition: An overpartition of n is a partition of n in which the first occurrence of a part may be overlined
Summary
In this paper we give some related definitions of overpartition, ( ), Pk (n), d(n), di,[4] (n), (n) and (n). We prove the four Theorems about overpartitions modulo 8 with certain conditions of n
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