Publications
My publications are listed below. You can also view them on Mathscinet.
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.
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 Alladi’s 60th birthday), Springer Proceedings in Mathematics and Statistics, 2017, pp. 39-57.
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
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.
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).
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).
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, Discrete Math 346 no. 2 (2023), 113224.
55. A modular relation involving a generalized digamma function and asymptotics of some integrals containing Xi(t)
Publications 2022 |A modular relation involving a generalized digamma function and asymptotics of some integrals containing Xi(t), Hardy-Ramanujan J. (2022), 140-151.
Publications 2023 | Explicit transformations for generalized Lambert series associated with the divisor function $\sigma_{a}^{(N)}(n)$ and their applications, Res. Math. Sci. 10, 38 (2023) (50 pages).
Publications 2022 | Two general series identities involving modified Bessel functions and a class of arithmetical functions, Canad. J. Math. 75 no. 6 (2023), 1800-1830.
58. Extended higher Herglotz functions I: Functional equations
Publications 2021 | Extended higher Herglotz functions I: Functional equations, Adv. Appl. Math. 153 (2024), 102622 (41 pages).
59. Applications of the Lipschitz summation formula and a generalization of Raabe’s cosine transform
Publications 2022 |Applications of the Lipschitz summation formula and a generalization of Raabe’s cosine transform, Constr. Approx. (2023) (40 pages).
60. 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), Canad. J. Math. (2023) (36 pages) (DOI: https://doi.org/10.4153/S0008414X23000597)
61. Ramanujan and Koshliakov meet Abel and Plana
Publications 2021 | Ramanujan and Koshliakov meet Abel and Plana, to appear in Some contributions to number theory and beyond: Proceedings of the centenary symposium for M V Subbarao, Fields Institute Communications, Baskar Balasubramanyam, Kaneenika Sinha and Mathukumalli Vidyasagar eds.
Publications 2023 | Modified Bessel functions in analytic number theory, to appear in the volume commemorating Richard Askey, Springer.
Publications 2023 | Modular relations for generalized digamma functions, J. Math. Anal. Appl. 539 no. 1 (2024), 128479 (37 pages).
A. Dixit
Publications 2023 | Recent developments pertaining to Ramanujan’s formula for odd zeta values, Expo. Math. 42 (2024), no. 5, Paper No. 125602 (23 pages).
65. Voronoi summation formula for the generalized divisor function $\sigma_z^{(k)}(n)$
Publications 2023 | Voronoi summation formula for the generalized divisor function $\sigma_z^{(k)}(n)$, submitted for publication.
66. Mordell-Tornheim zeta functions and functional equations for Herglotz-Zagier type functions
A. Dixit, S. Sathyanarayana and N. Guru Sharan
Publications 2024 | Mordell-Tornheim zeta functions and functional equations for Herglotz-Zagier type functions, submitted for publication.
67. Voronoi summation formulas, oscillations of Riesz sums, and Ramanujan-Guinand and Cohen type identities
S. Chorge and A. Dixit
Publications 2024 | Voronoi summation formulas, oscillations of Riesz sums, and Ramanujan-Guinand and Cohen type identities, submitted for publication.
68. The Rogers-Ramanujan dissection of a theta function
A. Dixit and G. Kumar
Publications 2024 | The Rogers-Ramanujan dissection of a theta function, submitted for publication.
1. The integrals in Gradshteyn and Ryzhik. Part 28. The confluent hypergeometric function and Whittaker functions
Expository papers 2015 | The integrals in Gradshteyn and Ryzhik. Part 28. The confluent hypergeometric function and Whittaker functions (with V. H. Moll), Scientia, Series A, 26 (2015), 49-61
2. The integrals in Gradshteyn and Ryzhik. Part 30. Trigonometric functions
Expository papers 2017 | The integrals in Gradshteyn and Ryzhik. Part 30. Trigonometric functions, Scientia, Series A, 27 (2016), 47-74.
3. Ramanujan’s paper on Riemann’s functions xi(s) and Xi(t) and a transformation from the Lost Notebook
Expository papers 2020 | Ramanujan’s paper on Riemann’s functions xi(s) and Xi(t) and a transformation from the Lost Notebook, to appear in the Encyclopedia of Srinivasa Ramanujan and His Mathematics.
4. Ramanujan’s published papers on definite integrals
Expository papers 2020 | Ramanujan’s published papers on definite integrals, to appear in the Encyclopedia of Srinivasa Ramanujan and His Mathematics.
5. Elliptic and related integrals
Expository papers 2020 | Elliptic and related integrals, to appear in the Encyclopedia of Srinivasa Ramanujan and His Mathematics.
6. Beautiful integrals
Expository papers 2020 | Beautiful integrals, to appear in the Encyclopedia of Srinivasa Ramanujan and His Mathematics.
7. Ramanujan’s beautiful integrals
Expository papers 2020 | Ramanujan’s beautiful integrals, Hardy-Ramanujan J. 43 (2020), 69-82.
8. Fifty golden years with Ramanujan: Bruce Berndt in conversation with Atul Dixit
Expository papers 2020 | Fifty golden years with Ramanujan: Bruce Berndt in conversation with Atul Dixit, Bhavana. The mathematics magazine, 8 No. 4 October 2024, 5-18.
1. Ramanujan at Elementary Levels: Glimpses
Books 2017 | Authors – V. R. Thiruvenkatachar and K. Venkatachaliengar, Ramanujan Mathematical Society, Lecture Note Series, No. 24, 2016.
1. Fermatche Shevatche Prameya
Mathematical Notes 2004 | Fermatche Shevatche Prameya (in Marathi), English translation: Fermat’s Last Theorem, December 26, 2004