Partition identities arising from Somos’s theta function identities

Kumar, B. R. Srivatsa; Veeresha, R. G.

doi:10.1007/s11565-016-0261-z

Cited by 7 publications

(2 citation statements)

References 3 publications

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“…Further, Yattunan [22] has proved some of these identities of level 4, 6 and 8. Vasuki and Veeresha [21] proved all the twenty four identities of level fourteen and Srivatsa Kumar and Veeresha [15] obtained partition identities for the same. Srivatsa Kumar and Anu Radha [16] have given a proof of few Somos's identities of levels 10.…”

Section: Introductionmentioning

confidence: 85%

Some Somos’s theta function identities of level 6 and application to partitions

Kumar

Sharath²

2020

Publ Inst Math (Belgr)

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M. Somos discovered around 6200 theta function identities using PARI/GP scripts without offering the proof. He runs PARI/GP scripts and it works as a sophisticated programmable calculator. These identities highly resemble those of Ramanujan?s identities. Here we prove a few theta-function identities of level 6 discovered by Somos by using modular equations of degree 3 given by Ramanujan and further we extract some interesting combinatorial interpretations of colored partitions.

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Section: Introductionmentioning

confidence: 85%

Some Somos’s theta function identities of level 6 and application to partitions

Kumar

Sharath²

2020

Publ Inst Math (Belgr)

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“…K. R. Vasuki and R. G. Veeresha [16] too have proved the identities discovered by Somos of theta-function of a level 14. B. R. Srivatsa Kumar and R. G. Veeresha [12] have also succeeded in obtaining partition identities for the same. B. R. Srivatsa Kumar and D. Anu Radha [13] proved the identities of level 10 and obtained certain interesting partitions discovered by Somos.…”

Section: Introductionmentioning

confidence: 94%

Theta function identities of level 6 and their application to partitions

Kumar

Rajanna²,

Narendra³

2019

Filomat

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M. Somos has conjectured many theta function identities belonging to different levels. He has done so with the use of a computer but has not chosen to validate these identities. We find that the mentioned identities are analogous to those discovered by Srinivasa Ramanujan. The intent to prove some of the identities prepared by Somos concerning theta function identities of a level six and to also establish certain partition-theoretic interpretations of these identities which we have been successfully proved here.

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Certain Somos’s $$\varvec{P}$$ P – $$\varvec{Q}$$ Q type Dedekind

Kumar

Vidya

2018

Proc Math Sci

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Partition identities arising from Somos’s theta function identities

Cited by 7 publications

References 3 publications

Some Somos’s theta function identities of level 6 and application to partitions

Some Somos’s theta function identities of level 6 and application to partitions

Theta function identities of level 6 and their application to partitions

Certain Somos’s $$\varvec{P}$$ P – $$\varvec{Q}$$ Q type Dedekind

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