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

Manipal Institute of Technology, Manipal

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

3 Citations (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

General Mathematics

Access to Document

10.2298/PIM2022137S

Cite this

@article{3821af37785c44d793a47df622552235,

title = "SOME SOMOS'S THETA FUNCTION IDENTITIES OF LEVEL 6 AND APPLICATION TO PARTITIONS",

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",

doi = "10.2298/PIM2022137S",

language = "English",

volume = "108",

pages = "137--144",

journal = "Publications de l'Institut Mathematique",

issn = "0350-1302",

publisher = "Mathematical Institute of the Serbian Academy of Sciences and Arts",

number = "122",

}

TY - JOUR

T1 - SOME SOMOS'S THETA FUNCTION IDENTITIES OF LEVEL 6 AND APPLICATION TO PARTITIONS

AU - Kumar, Belakavadi Radhakrishna Srivatsa

AU - Sharath, Gururaj

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.

PY - 2020

Y1 - 2020

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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85098741370

UR - https://www.scopus.com/pages/publications/85098741370#tab=citedBy

U2 - 10.2298/PIM2022137S

DO - 10.2298/PIM2022137S

M3 - Article

AN - SCOPUS:85098741370

SN - 0350-1302

VL - 108

SP - 137

EP - 144

JO - Publications de l'Institut Mathematique

JF - Publications de l'Institut Mathematique

IS - 122

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this