The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Partitions with Congruence Conditions


Affiliations
1 S. V. University, Tirupati, A.P., India
     

   Subscribe/Renew Journal


Let m be a given natural number and a={a1, a2,..., ar}, 1 < a3<m/2, aj≠at,j≠t and let pa(n) denote the number of partitions of the natural number n into summands congruent to ± aj(mod m), aj∈a. In the present paper convergent series and asymptotic formulae are obtained for pa{n). Also for qa(n), the corresponding partition function with distinct summands, the corresponding results are obtained by the author-they are mentioned here omitting details.
Subscription Login to verify subscription
User
Notifications
Font Size


Abstract Views: 193

PDF Views: 0




  • Partitions with Congruence Conditions

Abstract Views: 193  |  PDF Views: 0

Authors

V. V. Subrahmanyasastri
S. V. University, Tirupati, A.P., India

Abstract


Let m be a given natural number and a={a1, a2,..., ar}, 1 < a3<m/2, aj≠at,j≠t and let pa(n) denote the number of partitions of the natural number n into summands congruent to ± aj(mod m), aj∈a. In the present paper convergent series and asymptotic formulae are obtained for pa{n). Also for qa(n), the corresponding partition function with distinct summands, the corresponding results are obtained by the author-they are mentioned here omitting details.