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1.
Krishnaswami Alladi 《The Ramanujan Journal》2009,20(3):253-256
We will interpret a partial theta identity in Ramanujan’s Lost Notebook as a weighted partition theorem involving partitions
into distinct parts with smallest part odd. A special case of this yields a new result on the parity of the number of parts
in such partitions, comparable to Euler’s pentagonal numbers theorem. We will provide simple and novel proofs of the weighted
partition theorem and the special case. Our proof leads to a companion to Ramanujan’s partial theta identity which we will
explain combinatorially. 相似文献
2.
Krishnaswami Alladi Alexander Berkovich 《Transactions of the American Mathematical Society》2002,354(7):2557-2577
This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at least two. Consequences of this include Jacobi's celebrated triple product identity for theta functions, Sylvester's famous refinement of Euler's theorem, as well as certain weighted partition identities. Next, by studying partitions with prescribed bounds on successive ranks and replacing these with weighted Rogers-Ramanujan partitions, we obtain two new sets of theorems - a set of three theorems involving partitions into parts (mod 6), and a set of three theorems involving partitions into parts (mod 7), .
3.
Krishnaswami Alladi 《Proceedings Mathematical Sciences》1975,81(6):245-251
We discuss necessary and sufficient conditions for the partition of integer arithmetic sequences by sets generated by the multiples of irrational numbers by members of other arithmetic sequences. 相似文献
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The cascade theory of cosmic ray showers including ionisation loss is dealt with on the basis of the new approach suggested by us in an earlier contribution and an explicit Mellin transform solution is obtained for the mean number of particles produced in an infinite thickness of matter. 相似文献
7.
Krishnaswami Alladi 《Journal of Number Theory》1977,9(4):436-451
We study in this paper a new duality identity between large and small prime factors of integers and its relationship with the prime number theorem for arithmetic progressions. The asymptotic behavior of large prime factors of integers leads to interesting relations involving the Möbius function. 相似文献
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