On Somos’s theta-function identities of level 14

Vasuki, K. R.; Veeresha, R. G.

doi:10.1007/s11139-015-9714-8

Cited by 10 publications

(4 citation statements)

References 3 publications

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“…B. Yuttanan [17] has used Ramanujan's modular equations to prove identities of level 4, 6 and 8 for those of Somos theta-functions. 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.…”

Section: Introductionmentioning

confidence: 71%

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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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Section: Introductionmentioning

confidence: 71%

“…Since the proof of Somos Dedekind η-function identities of level 6 are similar, we omit the proof of the following identities. = 0. f 10 1 f 6 3 f 4 6 + 8 16 2 f 8 3 = 0. and many more.…”

Section: Remarkmentioning

confidence: 99%

Theta function identities of level 6 and their application to partitions

Kumar

Rajanna²,

Narendra³

2019

Filomat

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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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“…He has a large list of η -product identities and he runs PARI/GP scripts to look at each identity in P − Q forms. Recently Yuttanan [6] proved certain Somos theta-function identities of different levels by employing Ramanujan's modular equations and deduced certain partition identities for them, and Vasuki and Veeresha [5] proved η -function identities of level 14 discovered by Somos. Somos discovered sixty new elegant η -function identities of level 10.…”

Section: Introductionmentioning

confidence: 99%