Dr. K. SUSHAN BAIRY Assistant Professor

Specialization

Theory of Numbers, q-series, Modular equations, Class invariants, Continued fractions, theory of partitions.

Programs Organised

Qualification

Ph.D, 2012, Bangalore University

Teaching Experience

Vijaya College, R.V. Road, Bengaluru, Assistant Professor & Coordinator, 10 YEARS

MCA Department, Bangalore University, Guest Faculty, 6 Months

Government Science College, Nrupatunga Road, Bengaluru, Guest Faculty, 3 Years

Awards & Recognition

• Best Research Article presented award, International Conference on Emerging Trends in Mathematical Sciences, July 25-26, 2014, Vijayanagara Sri Krishnadevaraya University, Bellary. ``New identities for Ramanujan's cubic continued fraction''.

Publications In Refereed Journals

• On some modular equations of degree three found in Ramanujan’s second notebook, S. Mahadeva Naika, M. C. Maheshkumar and K. Sushan Bairy, J. Anal. Comput., 2(1), 2006, 45-49.
• Certain quotient of eta-function identities, S. Mahadeva Naika, M. C. Maheshkumar and K. Sushan Bairy, Adv. Stud. Contemp. Math., 16(1), 2008, 121-136.
• On some remarkable product of theta-function, S. Mahadeva Naika, M. C. Maheshkumar and K. Sushan Bairy, Aust. J. Math. Anal. Appl., 5(1), 2008, Art. 13, 1-15.
• On some new explicit evaluations of class invariants, S. Mahadeva Naika and K. Sushan Bairy, Vietnam J. Math., 36(1), 2008, 103-124.
• General formulas for explicit evaluations of Ramanujan’s cubic continued fraction, S. Mahadeva Naika, M. C. Maheshkumar and K. Sushan Bairy, Kyungpook Math. J., 49(3), 2009, 435-450.
• Some theorems on the explicit evaluations of singular moduli, Sushan Bairy, General Mathematics, 17(1), (2009), 71-87.
• On some Ramanujan-Selberg continued fraction, S. Mahadeva Naika, Remy Y. Denis and K. Sushan Bairy, Indian J. Math., 51(3), 2009, 585-596.
• Modular equations for the ratios of Ramanujan’s theta function ψ and evaluations, S. Mahadeva Naika, S. Chandankumar and K. Sushan Bairy, New Zealand J. Math., 40, 2010, 33-48.
• Some new modular equations of degree four and their explicit evaluations, S. Mahadeva Naika, K. Sushan Bairy and M. Manjunatha, Eur. J. Pure Appl. Math., 3(6), 2010, 924-947.
• On some parameter involving Ramanujan’s cubic continued fraction, S. Mahadeva Naika, S. Chandankumar and K. Sushan Bairy, Indian J. Math., 53(3), 2011, 495-509.
• On some new Schläfli-type mixed modular equations, S. Mahadeva Naika and K. Sushan Bairy, Adv. Stud. Contemp. Math., 21(2), 2011 189-206.
• A continued fraction of order 4 found in Ramanujan’s ‘lost’ notebook, S. Mahadeva Naika, K. Sushan Bairy and M. Manjunatha, South East Asian J. Math. Math. Sci., 9(3), 2011, 43-63.
• Certain identities for a continued fraction of Eisenstein, S. Mahadeva Naika, K. Sushan Bairy and M. Manjunatha, Far East J. Math. Sci., 57(2), 2011, 205-226.
• Class invariants and its applications, S. Mahadeva Naika and K. Sushan Bairy, Proceedings of the National Conference on Geometry, Algebra, Logic and Number Theory, Applications, Tumkur University, December 2012, 72-99. (ISBN: 978-81-924393-4-1).
• New identities for Ramanujan’s cubic continued fraction, S. Mahadeva Naika, S. Chandankumar and K. Sushan Bairy, Funct. Approx. Comment. Math., 46(1), 2012, 29-44.
• On some new identities for Ramanujan’s cubic continued fraction, S. Mahadeva Naika, S. Chandankumar and K. Sushan Bairy, Int. J. Contemp. Math. Sci., 7(20), 2012, 953-962.
• Some new identities for a continued fraction of order 12, S. Mahadeva Naika, S. Chandankumar and K. Sushan Bairy, South East Asian J. Math. Math. Sci., 10(2), 2012, 129-140.
• Some modular equations in the form of Schläfli, S. Mahadeva Naika and K. Sushan Bairy, Italian J. Pure Appl. Math., 30, 2013 233-252.
• Contributions to modular equations and class invariants, Sushan Bairy, Ph.D. Thesis, Bangalore University, 2011; Lambert Academic Publishing, Germany, 2013. (ISBN: 978-3-659-23898-7).
• Certain identities for a continued fraction of Ramanujan, S. Mahadeva Naika, K. Sushan Bairy and S. Chandankumar, Adv. Stud. Contemp. Math., 24(1), 2014, 45-66.
• On some explicit evaluation of the ratios of Ramanujan’s theta-function, S. Mahadeva Naika, K. Sushan Bairy and S. Chandankumar, Bull. Allahabad Math. Soc., 29(1), 2014, 53-86.
• A recurrence relation related to the product and successors of a known four-variable elementary identity, Bhargava and K. Sushan Bairy, Proceedings Jangjeon Math. Soc., 17(2), 2014, 273-286.
• Certain modular relations for remarkable product of theta-functions, S. Mahadeva Naika, K. Sushan Bairy and N. P. Suman, Proc. Jangjeon Math. Soc., 17(3), 2014, 317-331.
• Some new modular equations of degree 2 akin to Ramanujan, S. Mahadeva Naika, K. Sushan Bairy and S. Chandankumar, Southeast Asian Bulletin of Mathematics, 39(1), 2015, 93-112.
• Modular relations for a remarkable product of theta functions and evaluations, S. Mahadeva Naika, K. Sushan Bairy and N. P. Suman, Recent Advances in Mathematics, RMS-Lecture Notes Series, 21, 2015, 133-145.
• Jacobi-Sohncke-type mixed modular equations and their applications, S. Mahadeva Naika, K. Sushan Bairy and C. Shivashankar, Note di Matematica, 36(1), 2016, 37-54.
• Jacobi-Sohncke type mixed modular equations and their applications to overpartitions, S. Mahadeva Naika, K. Sushan Bairy, D. S. Gireesh, and N. P. Suman, Palestine J. Math., 6(1), 2017, 228-237.
• New identities for ratios of Ramanujan’s theta function, S. Mahadeva Naika, S. Chandankumar and K. Sushan Bairy, Adv. Stud. Contemp. Math. (Kyungshang), 27(1), 2017, 131-146.