FACULTY PROFILE. Research Areas : Special Functions, Number Theory, Partition Theory, Discrete Mathematics and Graph Theory.

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1 FACULTY PROFILE 1. Name : Dr. Chandrashekara Adiga 2. Designation : Professor 3. Qualification : M.Sc. Ph.D. 4. Area of Specialization: Special Functions, Number Theory, Partition Theory, Discrete Mathematics and Graph Theory. Research Areas : Special Functions, Number Theory, Partition Theory, Discrete Mathematics and Graph Theory. No. of Research publications : 88. List of Publications INTERNATIONAL: A simple proof for finite double series representations for the Bernoulli, Euler and Tangent Numbers., Int.J.Math.Edu.Sci,Technol. (U.K.) vol.14 Nos. 5(1983) C.Adiga (with S.Bhargava) On some Continued fraction identities of Srinivasa Ramanujan, Proc.Amer,Math.Soc. Vol.92 No.1 (1984) C.Adiga (with S.Bhargava). Two generalizations of Ramanujan's continued fraction identities,lecture Notes in Mathematics. Springer-Verlag, Vol.1122,(1984) C.Adiga (with S.Bhargava). Chapter 16 of Ramanujan's Second Note Book: Theta functions and Q.Series. Mem.Amer,Math. Soc. Vol.53 Vol.315(1985) 1-85 C.Adiga (with B.C.Berndt, S.Bhargava & G.N.Watson) On two elliptic θ- function identities stated by Srinivasa Ramanujan Int.J.Math.Edu.Sci,Technol. (U.K.) Vol.18 No.2 (1987) C.Adiga (with S.Bhargava ) Simple proofs of Jacobi's two and four square theorems. Int.J.Math.Edu.Sci,Technol. (U.K.) Vol.18 No.2 (1987) C.Adiga (with S.Bhargava ) 7. An estimate of Ramanujan related to the greatest integer function.bull Austral Math.Soc.Vol.44.No.1(1991) C.Adiga (with S.Bhargava and A generalization of Shiokawa's Rational Approximations to Roger's-Ramanujan Continued Fraction.Commentary Mathematici,Vol.41. No.2(1992) C.Adiga (with S.Bhargava and On the representations of an integer as a sum of two or four triangular numbers.nihonkai Math. Hiyr,Vol.3 No.2 (1992) C.Adiga.

2 Ramanujan's 1 1 Summation and an interesting convolution identity.bull Austral, Math.Soc.Vol.47,No.1(1993) C.Adiga (with S.Bhargava and On the representations of an integer as a sum of square and thrice a square.int.j.math.educ.sci, Technol.Vol.24,No.3(1993) C.Adiga (with S.Bhargava and Three square theorem as an application on Andrew's identity. Fibonacci Quarterly, May(1993) C.Adiga (with S.Bhargava and Jacobi's two square and four square theorems via. Roger's identity.tamkang Jour.Math.Vol.25.No.1(1994)23-27.C.Adiga. A basic bilateral series summation formula and its applications.integral Transforms and Special Functions, Vol.2 No.3 (1994) C.Adiga (with S.Bhargava ). A note on q-gamma and q-beta functions, Mathematica Balkanica, Vol.9 (1995) C.Adiga. Ramanujan's summation formula and its applications,proceedings of the International Conference on Transcedental Number Theory,Tokyo, 3-5 Dec(1996)8-26.C.Adiga. On some Rogers-Ramanujan type continued fraction identities,mathematica Balkanica, New Series Vol.12,(1998) Nos. -2,37-45.C.Adiga (with On some new identities involving integrals of theta-functions,advanced Studies in contemporary Mathematics V0l.3 o.2(2001)1-11.c.adiga (with K.R.Vauki and M.S.Mahadeva Naika). Some new explicit evaluations of Ramanujan's Cubic Continued fraction,new Zealand Jour. Math Vol.13(2002), C.Adiga (with K.R.Vauki and M.S.Mahadeva Naika). Ramanujan's remarkable summation formula as a 2-parameter generalization of the quintuple product identity,tamkang Jounal ofmathematics, Vol.33,No.3,(2002), C.Adiga (with S.Bhargava and M.S.Mahadeva Naika). A new class of modular equation akin to Ramanujan's P-Q eta-function identities and some evaluations there from,advanced Studies in contemporary Mathematics,(Kyungshang)Vol.5,1(2002).no.1,21-34.C.Adiga (with S.Bhargava and M.S.Mahadeva Naika). On a generalization of Sandor's functions Proc. Jangjeon Math.Soc.Vol.5,No.2 (2002) C.Adiga (with T.Kim). Common fixed points for sequence of mappings, Proc.Jangjeon Math. Soc. Vol.5, No.1(2002)21-34.C.Adiga (with iniswamy)24. A note on the values of (2k + 1),Advanced studies in contemporary Mathematics, Vol.5, o.2(2002) c.adiga (with L.C.Jang,T.Kim,Y.H.Kim,H.K.Pate and D.W.Park). Some theta function identities and new explicit evaluation of Rogers-Ramanujan continued fraction, Tamsui Oxfor Jour. ath. Sci. Vol.18 No.1(2002) C.Adiga (with K.R.Vauki and K.Shivashankara). Continued fraction representations for theta functions,proc. Jnagjeon Math. Soc. Vol.5, No.2(2002), , NNTDM 9(2003),7-12.C.Adiga (with T.Kim,D-W.Parts, Y.S.Ro and L-C Jang) A fixed point theorem on some non expansive type mappings on complete metric spaces. Fixed Point Theory and Applications Vol.4, (2003) 1-9. C.Adiga (with Giniswamy) On a continued fraction of Ramanujan, Tamsui Oxford Jour. Math. Sci. Vol.19, No.1 (2003) C.Adiga (with T.Kim)

3 Modular equations in the theory of signature 3 and P-Q identities, Advanced Studies in Contemporary Mathematics 7 (2003)No.1, C.Adiga (with T.Kim and Mahadeva Naika). On a q-analogue of Sandor's function.j. Inequal, Pure and Applied Math.4(4)(2003)1-5 C.Adiga (with T.Kim,D.D.Somashekara and Syed Noor Fathima ). On some transformation formulas for basic bilateral hypergeometric series, Proc. Of 14 th International Conference of the Jangjeon Mathematical Society C.Adiga (with D.D.Somashekar and Syed Noor Fathima) A note on strongly multiplicative graphs, Discussions mathematicae Graph Theory, 24(2004) C.Adiga (with D.D.Somashekar and H.N.Ramaswamy) General relations between sums of squares and sums of triangular numbers, Discrete Mathematics C.Adiga (with Shaun Cooper and Jung Hun Han). Sums of products of generalized Bernoulli Numbers, Int. J. Math. Vol.5, No.1 (2004) 1-7. C. Adiga (With T. Kim). On a certain class of add-even partitions, Proc. Jangjeon Math. Soc. 7(2004) No 2, C. Adiga (with S. Bhargava and A.K.Agarwal) A Note on a Certain Continued fraction of Ramanujan Bull. Austral. Math. Soc. 70 (2004), C. Adiga (with N. Anitha). On transformation of basic bilateral series, Proc. Jangjeon Math. Soc, 8 (2005) No 1, C. Adiga (with D.D.Somashekara and S,N.Fathima). A new approach to Jacobi's theorems via Ramanujan's continued fractions, Bull. Austral. Math. Soc. Vol. 71(2005) C. Adiga (with Jung Hun Han). A. General relation between sums of squares and sums of triangular numbers, Int. Jour. Number theory Vol. 1. No. 2 (2005) C. Adiga (with Shaun Cooper and Jung Hun Han). On the q-analogue of Gamma function and related inequalities I. Inequal. Pure and Applied Math Vol. 6 No 4 (2005) 1-8.C.Adiga (with Taekyun Kim). On some continued fractions of Ramanujan, Adv. Stud. Cont. Math., No.1, 12(2006), C.Adiga (with N. Anitha). On a reciprocity of Ramanujan, Tamsui Oxford J. Math. Sci., Vol. 22 No.1, (2006), 9-15.C.Adiga (with N. Anitha). An upper bound for maximum number of edges in a strongly multiplicative graph, Discussiones Mathematicae Graph Theory, 26(2006), 1-5. C.Adiga (with M. Smitha). On colorings of strongly multiplicative and strongly quotient graphs, Adv. Stud. Cont. Math., Vol. 13 No.2, (2006), C.Adiga (with R. K. Zaferani). More graphs whose energy exceeds the number of vertices, Iranian Journal of Mathematical Sciences and Informatics, Vol. 2 No.2, (2007), C.Adiga (with Zeynab Khoshbakht and I. Gutman). Upper bounds for energy of a graph, Adv. Stud. Cont. Math., Vol. 16 No.2, (2008), C.Adiga (with R. K. Zaferani). A note on certain divisibility problem, Int. Jour. Math. Analysis, Vol 2 No.24, (2008), C.Adiga (with H. N. Ramaswamy). Biregular graphs whose energy exceeds the number of vertices, MATCH Communications in Mathematical and in Computer Chemistry, No. 3, Volume 62(2009) C.Adiga (with I. Gutman, Antoaneta Klobucar and Snjezana Majstorovic). 49. On Maximum degree energy of a graph, International Journal of Contemporary Mathematical Sciences, Vol. 4, 2009, No. 8, C.Adiga (with M. Smitha).

4 On strongly sum difference quotient graphs, Advanced Studies in Contemporary Mathematics, 19 (2009), No. 1, pp C.Adiga (with C. S. S. Swamy). On the Skew Laplacian Energy of a digraph, International Mathematical Forum, 4, 2009, no. 39, C.Adiga (with M. Smitha). On the Skew energy of some unitary Cayley digraphs, Adv. Stud. Contemp. Math. 21. (Accepted for publication). C. Adiga (with H. N. Ramaswamy, D. D. Somashekara and Z. Khoshbakht). NATIONAL: A basic hypergeometric transformation of Ramanujan and generalization. Indian J.Pure, Appl.Maths.Vol.17 No.3 (1986) C.Adiga (with S.Bhargava). One some identities in the theory of elliptic functions found in the note books of Srinivasa Ramanujan. Mysore University Journal vol.no.xxx (1987) C.Adiga (with S.Bhargava). On some generalizations of Ramanujan's continued fraction identities. Proc.Ind. Acad Sci. Vol.97 (1987) C.Adiga (with S.Bhargava and On certain continued fractions related to 3 2 Basic Hypergeometric functions, Jour.Math.Sci,Vol.21, No.6(1987) C.Adiga (with S.Bhargava and Parity results deducible from certain theta function identities found in chapter of Ramanujan's second note book.math.student,vol.57,nos 1-4 (1989) C.Adiga (with S.Bhargava and Some relations between infinite series and infinite products, Proceedings of the symposium on Algebra and Number theory.cochin,india, 27-28, July (1990) 23-29,C.Adiga (with S.Bhargava and A note on Ward's conjecture. Jour.Ind.Math.Soc.Vol.59,(1993) C.Adiga(with N.R.Mohan). A note on Euler's totient function.jour.ind.math.soc.vol.62, Nos.1-4 (1996), ).C.Adiga (with H.N.Ramaswamy). Some interesting applications of Ramanujan's identities to representations of integersas sums of squares. Presented at 62 nd Annual Conference of IMS held at IIT Kanpur during Dec.1996.C.Adiga (with S.Bhargava and A note on rational approximations Presented at 62 nd Annual Conference of IMS held At IIT Kanpur during Dec C.Adiga (with D.D.Somashekara and K.R.Vasuki). A note on rational approximations. Jour.Ind.Math.Soc.Vol.65, Nos.1-4(1998), C.Adiga (with K.R.Vasuki). Number of representations of an integer as a sum of a square and five times a square.jour.ind.math.socl.vol.65 Nos. 1-4(1998) C.Adiga (with S.Bhargava and Ramanujan's 1 1 summation and an interesting generalization of an identity of Jacobi. Indian Jour.Math.Socl.Vol.41 Nos.1-4(1999) C.Adiga (with S.Bhargava and A fixed point theorem in four metric spaces, Jour.Nat and Phy, Sci,Vol.14,Nos. 1-2(2000) C.Adiga (with Giniswamy and S.L.Singh).

5 Some explicit evaluations of theta-functions, Far East J,Math. Sci, Vol.2(4)(2000), C.Adiga (with K.R.Vasuki ). On Some Continued fraction expansions for ratios of 2 2, Special Functions :Selected Articles, P.K.Banerji(Ed),Scientific Publisher, India, (2000) 1-16, Jodhpur,2001. C.Adiga (with R.Y.Denis and K.R.Vasuki ). On sums of triangular numbers, Math.Student, Vol.69,Nos.1-4(2001) 1-6. C.Adiga (with K.R.Vasuki ). Rogers- Ramanujan identities, continued Fractions, and their Generalizations, Selected Topics in Special functions, Eds, R.P.Agarwal, H.L.Manocha and K.Srinivasa Rao (2001), C.Adiga (with Strongly *- Graphs, Math. Forum Vol.XIII,( ), C.Adiga (with A fixed point theorem in a 2-metric space and an application, J.Nat. and Pht.Sci Vo.15, Nos.1-2(2001)55-64.C.Adiga (with Giniswamy and S.L.Singh). Contraction type mappings and convergence of sequences of fixed points in 2 -metric spaces, Proc.National Conf. On challenges of the 21 st Century in Mathematics and its allied topics, (2001), C.Adiga (with Giniswamy). On strongly multiplicative graphs, Proc. National Conf. On challenges of the 21 st Century in Mathematics and its allied topics, (2001) C.Adiga (with H.N.Ramaswamy and Integral representations and some explicit evaluations of a continued fraction of Ramanujan, J.P.Jour.Algebra, Number theory and Appl.Vol.2 No.1 (2002),5-20. C.Adiga(with M.S.Mahadeva Naika and Ramya Rao) On some P-Q eta-function identities of Ramnaujan, Indian Jour. Math. 44 (2002), no.3, C.Adiga (with M.S.Mahadeva Naika and K.Shivashankara). A new class of modular equations in Ramanujan's alternative theory of elliptic function of signature 4 and some new P-Q eta-function identities,indian Jour. Math.Vol.45, No.1 (2003) C. Adiga (With S. Bhargava and M. S. Mahadeva Naika). On Strongly multiplicative graphs, South East Asian J.Math. and Math.Sci,2(2003) C.Adiga(with D.D.Somashekara and H.N.Ramaswamy ). Transformations of Ramanujan's Summation formula and its applications, JAMA,Vol 1, No.1 (2005 )55-64.C.Adiga (With T.Kim and N. Anitha ) On Ramanujan's Cubic Continued Fraction and Explicit Evaluations of Theta Functions, Indian J. pure appl. Math. 35(9) (2004 ) C.Adiga (With T.Kim, M. S. Mahadeva Naika and H. S. Madhusudan) On a class of N-parity partition, Indian J. Math., No. 2-3, 47(2005 ) C.Adiga (With S. Bhargava and N. Anitha) New Partition theoretic facts of two identities of Euler, Indian J. pure appl. Math. 36(11) (2005 ) C.Adiga (With S. Bhargava and N. Anitha). On an identity of Euler, Journal of Applied Mathematical Analysis and Applications, Vol 2 No.2, (2006), C.Adiga (With P. S. Guruprasad). A generalization of Agarwal's Theorem, Ramanujan Math. Soc., Lecture Notes series No.2, (2006), C.Adiga (With N. Anitha and Jung Hun Han). General modular transformations for theta-functions, Indian J. Math. 49, No.2, (2007), C.Adiga (With M. S. Mahadeva Naika and Jung Hun Han).

6 Strongly quotient graphs, South East Asian J. Math. And Math. Sc., 15 No.2 (2007), C.Adiga (With R. K. Zaferani and M. Smitha). On a three variable reciprocity theorem, South East J. Math. And Math. Sc., Vol 6 No.2 (2008), C.Adiga (With P. S. Guruprasad). On modular relations for the functions analogous to Rogers-Ramanujan functions with applications to partitions, South East J. Math. And Math. Sc., Vol 6 No.2, (2008), C.Adiga (With K. R. Vasuki and B. R. Srivatsa Kumar).. PROCEEDINGS : Proceedings of the International Conference on The Works of Srinivasa Ramanujan (2001) C.Adiga (with. No. of Ph. D's guided - submitted : 01 No. of Ph. D's guided - awarded : 08 No. of Ph. D's guided - in progrees : 03