Ranganatha Dasappa
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View article: On a product of three theta functions and the number of representations of integers as mixed ternary sums involving squares, triangular, pentagonal and octagonal numbers
On a product of three theta functions and the number of representations of integers as mixed ternary sums involving squares, triangular, pentagonal and octagonal numbers Open
In this paper, we derive a general formula to express the product of three theta functions as a linear combination of other products of three theta functions. Moreover, we use the main formula to deduce a general formula for the product of…
View article: On some new arithmetic properties of certain restricted color partition functions
On some new arithmetic properties of certain restricted color partition functions Open
Very recently, Pushpa and Vasuki (Arab. J. Math. 11, 355–378, 2022) have proved Eisenstein series identities of level 5 of weight 2 due to Ramanujan and some new Eisenstein identities for level 7 by the elementary way. In their paper, they…
View article: Some new congruences for (s,t)-regular bipartition functions
Some new congruences for (s,t)-regular bipartition functions Open
Let Bs,t(n) denote the number of (s,t)-regular bipartitions of n. We prove several infinite families of congruences modulo t for Bs,t(n) where (s,t) ? {(2,7), (5?, 7), (3?, 11), (5?, 11), (3?, 17)}, ? ? 1.
View article: A Simple Proof of a Conjecture of Dou on (3,7)-Regular Bipartitions Modulo 3
A Simple Proof of a Conjecture of Dou on (3,7)-Regular Bipartitions Modulo 3 Open
See the abstract in the attached pdf.