Assistant Professor of Mathematics

Publications

 

1. Orthopoles and the Pappus Theorem

A. Dixit and D. Grinberg
Publications 2004 | Orthopoles and the Pappus Theorem, Forum Geom., 4, (2004), 53-59.

 

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

A. Dixit and A. Yu. Solynin
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

A. Dixit
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

A. Dixit
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

A. Dixit and B. C. Berndt
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

A. Dixit, B. C. Berndt and J. Sohn
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

A. Dixit
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

A. Dixit
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

A. Dixit, A. Roy and A. Zaharescu
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

A. Dixit
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

A. Dixit
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

A. Dixit, S. H. Chan and F. G. Garvan
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

A. Dixit and A. J. Yee
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

A. Dixit
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

A. Dixit, T. Amdeberhan, V. De Angelis, V. H. Moll and C. Vignat
Publications 2013 | From sequences to polynomials and back, via operator orderings, J. Math. Phys., 54, 123502 (2013)

 

16. Monotonicity results for Dirichlet L-functions

A. Dixit, A. Roy and A. Zaharescu
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

A. Dixit, V. H. Moll and C. Vignat
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

A. Dixit, T. Amdeberhan, X. Guan, L. Jiu and V. H. Moll
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

A. Dixit, M. Coffey, V. De Angelis, V. H. Moll, A. Straub and C. Vignat
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

A. Dixit and V. H. Moll
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

A. Dixit, N. Robles, A. Roy and A. Zaharescu
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

A. Dixit, A. Roy and A. Zaharescu
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

A. Dixit, L. Jiu, V. H. Moll and C. Vignat
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 $\phi(q)$

A. Dixit, G. E. Andrews and A. J. Yee
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

A. Dixit, A. Roy and A. Zaharescu
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

A. Dixit, N. Robles, A. Roy and A. Zaharescu
Publications 2016 | Koshliakov kernel and identities involving the Riemann zeta function, J. Math. Anal. Appl., 435, Issue 2 (2016), 1107–1128.

 

27. A hypergeometric inequality

A. Dixit, V. H. Moll and V. Pillwein
Publications 2016 | A hypergeometric inequality, Ann. Comb. 20 (2016), 65-72.

 

28. Asymptotics and exact formulas for Zagier polynomials

A. Dixit, M. L. Glasser, V. H. Moll and C. Vignat
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

A. Dixit, B. C. Berndt, A. Roy and A. Zaharescu
Publications 2017 | New Pathways and Connections in Number Theory and Analysis Motivated by Two Incorrect Claims of Ramanujan, Adv. Math. 304 (2017), 809-929.

 

30. Modified Norlund polynomials

A. Dixit, A. Kabza, V. H. Moll and C. Vignat
Publications 2017 | Modified Norlund polynomials, Ramanujan J. 42 (2017), 69-96.

 

31. Error functions, Mordell integrals and an integral analogue of partial theta function

A. Dixit, A. Roy and A. Zaharescu
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

A. Dixit, B. C. Berndt, S. Kim and A. Zaharescu
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 $\omega(q)$

A. Dixit, G. E. Andrews, D. Schultz and A. J. Yee
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

K. Banerjee and A. Dixit
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

A. Dixit, A. Kesarwani and V. H. Moll (with an Appendix by N. M. Temme)
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

A. Dixit, R. Kumar, B. Maji and A. Zaharescu
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

B. C. Berndt, A. Dixit, S. Kim and A. Zaharescu
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

A. Dixit
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

A. Dixit and R. Gupta
Publications 2019 | On squares of odd zeta values and analogues of Eisenstein series, Adv. Appl. Math. 110 (2019), 86-119..
 

40. Generalized Lambert series, Raabe's cosine transform and a generalization of Ramanujan's formula for $\zeta(2m+1)$

A. Dixit, R. Gupta, R. Kumar and B. Maji
Publications 2018 | Generalized Lambert series, Raabe's cosine transform and a generalization of Ramanujan's formula for $\zeta(2m+1)$, to appear in Nagoya Mathematical Journal.

 

40. Generalized Lambert series and arithmetic nature of odd zeta values

A. Dixit and B. Maji
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. A simple proof of a congruence for a series involving the little $q$-Jacobi polynomials

A. Dixit
Publications 2019 | A simple proof of a congruence for a series involving the little $q$-Jacobi polynomials, to appear in Annals of Combinatorics (Special issue in honor of George E. Andrews' 80th birthday). (DOI: https://doi.org/10.1007/s00026-019-00456-5 )

 

43. Partition implications of a new three parameter $q$-series identity

A. Dixit and B. Maji
Publications 2018 | Partition implications of a three parameter $q$-series identity, Ramanujan Journal (2019), 1-36 (DOI: https://doi.org/10.1007/s11139-019-00177-6).

 

44. Untrodden pathways in the theory of the restricted partition function $p(n, N)$

A. Dixit, P. Eyyunni, B. Maji and G. Sood
Publications 2018 | Untrodden pathways in the theory of the restricted partition function $p(n, N)$, submitted for publication.

 

45. Analogue of a Fock-type integral arising from electromagnetism and its applications in number theory

A. Dixit and A. Roy
Publications 2019 | Analogue of a Fock-type integral arising from electromagnetism and its applications in number theory, submitted for publication.

 

46. On Hurwitz zeta function and Lommel functions

A. Dixit and R. Kumar
Publications 2019 | On Hurwitz zeta function and Lommel functions, submitted for publication.
-->

Expository Papers

 
 

1. The integrals in Gradshteyn and Ryzhik. Part 28. The confluent hypergeometric function and Whittaker functions

A. Dixit and V. H. Moll
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

A. Dixit, T. Amdeberhan, X. Guan, L. Jiu, A. Kuznetsov, V. H. Moll and C. Vignat
Expository papers 2017 | The integrals in Gradshteyn and Ryzhik. Part 30. Trigonometric functions, Scientia, Series A, 27 (2016), 47-74.

Books

 
 

1. Ramanujan at Elementary Levels: Glimpses

A. Dixit, B. C. Berndt, V. J. Reuter, P. Xu, and B. Yuttanan (eds.)
Books 2017 | Authors - V. R. Thiruvenkatachar and K. Venkatachaliengar, Ramanujan Mathematical Society, Lecture Note Series, No. 24, 2016.

Mathematical Notes

 
 

1. Fermatche Shevatche Prameya

A. Dixit
Mathematical Notes 2004 | Fermatche Shevatche Prameya (in Marathi), English translation: Fermat's Last Theorem, December 26, 2004