**2. Monotonicity of quotients of theta functions related to an extremal problem on harmonic measure**

Publications

**2007**| Monotonicity of quotients of theta functions related to an extremal problem on harmonic measure J. Math. Anal. Appl., 336, No. 2, (2007), 1042-1053.**3. The Laplace transform of the psi function**

Publications

**2010**| The Laplace transform of the psi function, Proc. Amer. Math. Soc., 138, No. 2 (2010), 593-603.** 4. Series transformations and integrals involving the Riemann $\Xi$-function**

Publications

**2010**| Series transformations and integrals involving the Riemann $\Xi$-function, J. Math. Anal. Appl., 368, (2010), 358-373.** 5. A transformation formula involving the Gamma and Riemann zeta functions in Ramanujan's Lost Notebook**

Publications

**2010**| A transformation formula involving the Gamma and Riemann zeta functions in Ramanujan's Lost Notebook, The legacy of Alladi Ramakrishnan in the mathematical sciences, K. Alladi, J. Klauder, C. R. Rao, Eds, Springer, New York, 2010, pp.199-210.**6. Character analogues of theorems of Ramanujan, Koshliakov and Guinand**

Publications

**2011**| Character analogues of theorems of Ramanujan, Koshliakov and Guinand, Adv. Appl. Math., 46, Issues 1-4, (2011), 54-70 (Special issue in honor of Dennis Stanton).**7. Analogues of a transformation formula of Ramanujan**

Publications

**2011**| Analogues of a transformation formula of Ramanujan, Int. J. Number Theory, 7, No. 5 (2011), 1151-1172.**8. Transformation formulas associated with integrals involving the Riemann $\Xi$-function**

Publications

**2011**| Transformation formulas associated with integrals involving the Riemann $\Xi$-function, Monatsh. Math., 164, No. 2 (2011), 133-156.**9. Convexity of quotients of theta functions**

Publications

**2012**| Convexity of quotients of theta functions, J. Math. Anal. Appl., 386, No. 1, (2012), 319-331.**10. Character analogues of Ramanujan type integrals involving the Riemann $\Xi$-function**

Publications

**2012**| Character analogues of Ramanujan type integrals involving the Riemann $\Xi$-function, Pacific J. Math., 255, No. 2 (2012), 317-348.**11. Analogues of the general theta transformation formula**

Publications

**2013**| Analogues of the general theta transformation formula, Proc. Roy. Soc. Edinburgh, Sect. A, 143 (2013), 371-399.**12. Rank-Crank type PDEs and generalized Lambert series identities**

Publications

**2013**| Rank-Crank type PDEs and generalized Lambert series identities, Ramanujan J., 31, Issue 1-2 (2013), 163-189 (Special issue in honor of Mourad Ismail and Dennis Stanton) pdf.**13. Generalized higher order spt-functions**

Publications

**2013**| Generalized higher order spt-functions, Ramanujan J., 31, Issue 1-2 (2013), 191-212 (Special issue in honor of Mourad Ismail and Dennis Stanton) pdf.**14. Ramanujan's ingenious method for generating modular-type transformation formulas**

Publications

**2013**| Ramanujan's ingenious method for generating modular-type transformation formulas, The Legacy of Srinivasa Ramanujan, RMS-Lecture Note Series No. 20, (2013), pp. 163-179.**15. From sequences to polynomials and back, via operator orderings**

Publications

**2013**| From sequences to polynomials and back, via operator orderings, J. Math. Phys., 54, 123502 (2013)**16. Monotonicity results for Dirichlet L-functions**

Publications

**2014**| Monotonicity results for Dirichlet L-functions, J. Math. Anal. Appl., 410, No. 1, (2014), 307-315.**17. The Zagier modification of Bernoulli numbers and a polynomial extension. Part I**

Publications

**2014**| The Zagier modification of Bernoulli numbers and a polynomial extension. Part I., Ramanujan J., 33, No. 3 (2014), 379-422.**18. The unimodality of a polynomial coming from a rational integral. Back to the original proof**

Publications

**2014**| The unimodality of a polynomial coming from a rational integral. Back to the original proof, J. Math. Anal. Appl., 420 (2014), 1154-1166.**19. The Zagier polynomials. Part II. Arithmetic properties of coefficients**

Publications

**2014**| The Zagier polynomials. Part II. Arithmetic properties of coefficients, Ramanujan J., 35, Issue 3 (2014), 361-390.**20. Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations**

Publications

**2015**| Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations, J. Number Theory 147 (2015), 211-249.**21. Zeros of combinations of the Riemann $\xi$-function on bounded vertical shifts**

Publications

**2015**| Zeros of combinations of the Riemann $\xi$-function on bounded vertical shifts, J. Number Theory 149 (2015), 404-434.**22. Ramanujan-Hardy-Littlewood-Riesz phenomena for Hecke forms**

Publications

**2015**| Ramanujan-Hardy-Littlewood-Riesz phenomena for Hecke forms, J. Math. Anal. Appl. 426 (2015), 594-611.** 23. The finite Fourier transform of classical polynomials**

Publications

**2015**| The finite Fourier transform of classical polynomials, J. Austral. Math. Soc. 98 No. 2 (2015), 145-160.**24. Partitions associated with the Ramanujan/Watson mock theta functions $\omega(q)$, $\nu(q)$ and $\phi(q)$**

Publications

**2015**| Partitions associated with the Ramanujan/Watson mock theta functions $\omega(q)$, $\nu(q)$ and $\phi(q)$, Research in Number Theory 1, Issue 1 (2015), 1-25.**25. Riesz-type criteria and theta transformation analogues**

Publications

**2016**| Riesz-type criteria and theta transformation analogues, J. Number Theory 160 (2016), 385-408.**26. Koshliakov kernel and identities involving the Riemann zeta function**

Publications

**2016**| Koshliakov kernel and identities involving the Riemann zeta function, J. Math. Anal. Appl., 435, Issue 2 (2016), 1107–1128.**28. Asymptotics and exact formulas for Zagier polynomials**

Publications

**2016**| Asymptotics and exact formulas for Zagier polynomials, Research in Number Theory, 2 (1) (2016), 1-26.**29. New Pathways and Connections in Number Theory and Analysis Motivated by Two Incorrect Claims of Ramanujan**

Publications

**2017**| New Pathways and Connections in Number Theory and Analysis Motivated by Two Incorrect Claims of Ramanujan, Adv. Math. 304 (2017), 809-929.**31. Error functions, Mordell integrals and an integral analogue of partial theta function**

Publications

**2017**| Error functions, Mordell integrals and an integral analogue of partial theta function, Acta Arith. 177 No. 1 (2017), 1-37.**32. On a theorem of A. I. Popov on sums of squares**

Publications

**2017**| On a theorem of A. I. Popov on sums of squares, Proc. Amer. Math. Soc. 145, No. 9 (2017), 3795-3808.**33. Overpartitions related to the mock theta function $\omega(q)$**

Publications

**2017**| Overpartitions related to the mock theta function $\omega(q)$, Acta Arith. 181, No. 3 (2017), 253-286.**34. New representations for $\sigma(q)$ via reciprocity theorems**

Publications

**2017**| New representations for $\sigma(q)$ via reciprocity theorems, in*Analytic Number Theory, Modular Forms and q-Hypergeometric Series (in honor of Krishnaswami A**lladi’s 60*, Springer Proceedings in Mathematics and Statistics, 2017, pp. 39-57.^{th}birthday)**35. A generalized modified Bessel function and a higher level analogue of the theta transformation formula **

Publications

**2018**| A generalized modified Bessel function and a higher level analogue of the theta transformation formula,*J. Math. Anal. Appl. 459 (2018), 385-418.***36. Zeros of combinations of the Riemann $\Xi$-function and the confluent hypergeometric function on bounded vertical shifts**

Publications

**2018**| Zeros of combinations of the Riemann $\Xi$-function and the confluent hypergeometric function on bounded vertical shifts, J. Math. Anal. Appl. 466 (2018), 307-323.**37. Sums of squares and products of Bessel functions**

**37. Sums of squares and products of Bessel functions**

Publications

**2018**| Sums of squares and products of Bessel functions,*Adv. Math.*338 (2018), 305-338.**38. Modular-type transformations and integrals involving the Riemann $\Xi$-function**

Publications

**2018**| Modular-type transformations and integrals involving the Riemann $\Xi$-function,*Math. Student*87 Nos. 3-4 (2018), 47-59.**39. On squares of odd zeta values and analogues of Eisenstein series**

Publications

**2019**| On squares of odd zeta values and analogues of Eisenstein series, Adv. Appl. Math. 110 (2019), 86-119..**40. A simple proof of a congruence for a series involving the little $q$-Jacobi polynomials**

Publications

**2019**| A simple proof of a congruence for a series involving the little $q$-Jacobi polynomials, Ann. Comb. 23 (2019), no. 3-4, 713-716 (Special issue in honor of George E. Andrews' 80th birthday).**41. Generalized Lambert series and arithmetic nature of odd zeta values**

Publications

**2017**| Generalized Lambert series and arithmetic nature of odd zeta values, Proceedings of the Royal Society of Edinburgh, Section A: Mathematics, 1-29 (2019).(**previously titled:**An extension of the Kanemitsu-Tanigawa-Yoshimoto theorem on a generalized Lambert series and its implications)**42. Partition implications of a new three parameter $q$-series identity**

Publications

**2018**| Partition implications of a three parameter $q$-series identity, Ramanujan Journal 52 (2020), 323-358.**43. Analogue of a Fock-type integral arising from electromagnetism and its applications in number theory**

Publications

**2019**| Analogue of a Fock-type integral arising from electromagnetism and its applications in number theory, Res. Math. Sci.,**7**, Article number: 25 (2020) (33 pages).**44. Generalized Lambert series, Raabe's cosine transform and a generalization of Ramanujan's formula for $\zeta(2m+1)$**

Publications

**2018**| Generalized Lambert series, Raabe's cosine transform and a generalization of Ramanujan's formula for $\zeta(2m+1)$, Nagoya Math. J.. 239 (2020), 232-293.**45. Untrodden pathways in the theory of the restricted partition function $p(n, N)$**

Publications

**2018**| Untrodden pathways in the theory of the restricted partition function $p(n, N)$, J. Combin. Theory Ser. A, 180 (2021), 105423 (49 pages).**46. On Hurwitz zeta function and Lommel functions**

Publications

**2019**| On Hurwitz zeta function and Lommel functions, Int. J. Number Theory 17 no. 2 (2021), 393-404.**47. Superimposing theta structure on a generalized modular relation**

Publications

**2020**| Superimposing theta structure on a generalized modular relation, Res. Math. Sci. 8 (2021) No. 3, Paper No. 41 (83 pages).**48. Koshliakov zeta functions I: Modular relations**

Publications

**2021**| Koshliakov zeta functions I: Modular relations, Adv. Math. 393 (2021), Paper No. 108093 (41 pages).**49. Generalizations of the Andrews-Yee identities associated with the mock theta functions omega(q) and nu(q)**

Publications

**2021**| Generalizations of the Andrews-Yee identities associated with the mock theta functions omega(q) and nu(q), J. Algebraic Combin. 55, no. 4 (2022), 1031-1062. (DOI: https://doi.org/10.1007/s10801-021-01082-2 ).**50. Explicit transformations of certain Lambert series**

Publications

**2020**| A generalized modified Bessel function and explicit transformations of certain Lambert series, Res. Math. Sci. 9, 34 (2022), (54 pages) (DOI: https://doi.org/10.1007/s40687-022-00331-5)**51. A modular relation involving non-trivial zeros of the Dedekind zeta function, and the Generalized Riemann Hypothesis**

Publications

**2021**| A modular relation involving non-trivial zeros of the Dedekind zeta function, and the Generalized Riemann Hypothesis, J. Math. Anal. Appl. 515, no. 2 (2022), 126435 (16 pages) (DOI: https://doi.org/10.1016/j.jmaa.2022.126435)**52. A class of identities associated with Dirichlet series satisfying Hecke's functional equation**

Publications

**2021**| A class of identities associated with Dirichlet series satisfying Hecke's functional equation, Proc. Amer. Math. Soc. 150, no. 11 (2022), 4785-4799.**53. Combinatorial identities associated with a bivariate generating function for overpartition pairs**

Publications

**2022**| Combinatorial identities associated with a bivariate generating function for overpartition pairs, Adv. Appl. Math. 143 (February 2023), 102444 (23 pages).**54. A finite analogue of a q-series identity of Bhoria, Eyyuni and Maji and its applications**

Publications

**2022**|A finite analogue of a q-series identity of Bhoria, Eyyuni and Maji and its applications, to appear in Discrete Mathematics.**55. Two general series identities involving modified Bessel functions and a class of arithmetical functions**

Publications

**2022**| Two general series identities involving modified Bessel functions and a class of arithmetical functions, to appear in Canadian Journal of Mathematics.**56. Ramanujan and Koshliakov meet Abel and Plana**

Publications

**2021**| Ramanujan and Koshliakov meet Abel and Plana, to appear in Proceedings of the birth centenary conference for Professor M. V. Subbarao, Fields Institute Communications, Baskar Balasubramanyam, Kaneenika Sinha and Mathukumalli Vidyasagar eds.**57. Extended higher Herglotz functions I: Functional equations**

Publications

**2021**| Extended higher Herglotz functions I: Functional equations, submitted for publication.**58. Lambert series of logarithm, the derivative of Deninger's function $R(z)$ and a mean value theorem for zeta(1/2-it)zeta'(1/2}+it)**

Publications

**2022**| Lambert series of logarithm, the derivative of Deninger's function $R(z)$ and a mean value theorem for zeta(1/2-it)zeta'(1/2}+it), submitted for publication.**59. Applications of Lipschitz summation formula and a generalization of Raabe's cosine transform**

Publications

**2022**|Applications of Lipschitz summation formula and a generalization of Raabe's cosine transform, submitted for publication.