SOME SOMOS'S THETA FUNCTION IDENTITIES OF LEVEL 6 AND APPLICATION TO PARTITIONS

Belakavadi Radhakrishna Srivatsa Kumar; Gururaj Sharath

doi:10.2298/PIM2022137S

SOME SOMOS'S THETA FUNCTION IDENTITIES OF LEVEL 6 AND APPLICATION TO PARTITIONS

Belakavadi Radhakrishna Srivatsa Kumar, Gururaj Sharath

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	137-144
Number of pages	8
Journal	Publications de l'Institut Mathematique
Volume	108
Issue number	122
DOIs	https://doi.org/10.2298/PIM2022137S
Publication status	Published - 2020

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.2298/PIM2022137S

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abstract = "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.",

author = "Kumar, {Belakavadi Radhakrishna Srivatsa} and Gururaj Sharath",

note = "Funding Information: 2010 Mathematics Subject Classification: Primary 11F27, 11P81. Key words and phrases: theta functions, modular equation, partitions. This work is partially supported by DST-SERB, Government of India EMR/2016/001601. ∗Corresponding author Publisher Copyright: {\textcopyright} 2020. All Rights Reserved.",

year = "2020",

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language = "English",

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journal = "Publications de l'Institut Mathematique",

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N1 - Funding Information: 2010 Mathematics Subject Classification: Primary 11F27, 11P81. Key words and phrases: theta functions, modular equation, partitions. This work is partially supported by DST-SERB, Government of India EMR/2016/001601. ∗Corresponding author Publisher Copyright: © 2020. All Rights Reserved.

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N2 - 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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SOME SOMOS'S THETA FUNCTION IDENTITIES OF LEVEL 6 AND APPLICATION TO PARTITIONS

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