The Journal of the Indian Mathematical Society

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Partitions with Congruence Conditions


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

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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.
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  • Partitions with Congruence Conditions

Abstract Views: 274  |  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.