Publications
(With B. C. Berndt and A. Zaharescu), Evaluations and relations for finite trigonometric sums, submitted.
(With B. C. Berndt and A. Zaharescu), Finite trigonometric sums arising from Ramanujan's theta functions, Ramanujan J., 63 (2024), 673-685..
(With B. C. Berndt and A. Zaharescu), Exact evaluations and reciprocity theorems for finite trigonometric sums, Research in the Mathematical Sciences, 10 (2023), 40.
(With B. C. Berndt, M. Fassina and A. Zaharescu), Two-parameter identities for divisor sums in algebraic number fields, J. Mathematical Analysis and Applications, 506 (2) (2022), 125679.
(With B. C. Berndt, M. Fassina and A. Zaharescu), Balanced derivatives, identities, and bounds for trigonometric and Bessel series, Advances in Math., 395 (2022), 108085.
(With M. Fassina and A. Zaharescu), The distribution of spacings between the fractional parts of $n^d\alpha$, International Mathematics Research Notices, 14 (2022), 10555--10585.
A combinatorial proof of a recurrence relation for the sum of divisors function, International J. Number Thy., (special issue dedicated to Bruce C. Berndt on the occasion of his 80th birthday) 17 No. 3 (2021), 647--653.
A generalization of modular equations of higher degrees, J. Combin. Thy. Ser. (A), 180 (2021), 105420.
Generalized colored partition identities, Annals of Combinatorics, 24 (3) (2020), 425--438.
(With G. E. Andrews, B. C. Berndt, S. H. Chen and A. Malik), Four identities for third order mock theta functions, Nagoya Math. Journal, 239 (2020), 173--204.
(With B. C. Berndt, A. Dixit and A. Zaharescu), Sums of squares and products of Bessel functions, Advances in Math., 338 (2018), 305--338.
Bressoud's conjecture, Advances in Math., 325 (2018), 770--813.
(With B. C. Berndt and A. Zaharescu), The circle problem of Gauss and the divisor problem of Dirichlet- still unsolved, Amer. Math. Monthly, 125 (2018), 99--114.
(With B. C. Berndt, A. Dixit and A. Zaharescu), On a theorem of A. I. Popov on sums of squares, Proceedings of the AMS., 145 (2017), 3795--3808.
Identities for trigonometric divisor sums, International J. Number Thy., 13, No. 4 (2017), 957-975.
Sums of divisors functions and Bessel function series, J. Number Thy., 170 (2017), 142--184.
(With B. C. Berndt and A. Zaharescu), Weighted divisor sums and Bessel function series V, J. Approximation Theory, (special issue dedicated to Dick Askey on the occasion of his 80th birthday), 197 (2015), 101--114.
(With B. C. Berndt), Logarithmic means and double series of Bessel functions, International J. Number Thy., (special issue: In memory of Paul T. Bateman and Heini Halberstam), 11 (2015), 1535--1556.}
(With B. C. Berndt), Identities for logarithmic means: A survey, in Advances in the Theory of Numbers: Proceedings of the Thirteenth Conference of the Canadian Number Theory Association, A. Alaca, S. Alaca, and K. S. Williams, eds., Fields Inst. Research Math. Sci., vol. 77, 2015, pp. 1--10.
(With A. J. Yee), Partitions with part difference conditions and Bressoud's conjecture, J. Combin. Thy. Ser. (A), 126 (2014), 35--69.
(With B. C. Berndt and A. Zaharescu), Analogues of Koshliakov's formula, in Ramanujan 125, Contemp. Math., 627, K. Alladi, F. Garvan, and A. J. Yee, editors, American Mathematical Society, Providence, RI, 2014, pp. 41--48
(With B. C. Berndt and A. Zaharescu), Diophantine approximation of the exponential function and Sondow's conjecture, Advances in Math., 248 (2013), 1298--1331.
(With B. C. Berndt and A. Zaharescu), Weighted divisor sums and Bessel function series III, J. Reine Angew. Math. (Crelle's Journal), 683 (2013), 67--96.
(With B. C. Berndt, M. T. Phaovibul and A. Zaharescu), Diophantine approximation with partial sums of power series, Acta Arithmetica, 161 (2013), 249--266.
(With B. C. Berndt), A problem in diophantine approximation found in Ramanujan's lost notebook, Ramanujan J., 31 (2013), 83--95.
(With B. C. Berndt and A. Zaharescu), Dirichlet L-functions, elliptic curves, hypergeometric functions, and rational approximation with partial sums of power series, Math. Research Letters, 20 No. 3 (2013), 429--448.
(With B. C. Berndt and A. Zaharescu), The circle and divisor problems, and double series of Bessel functions, Advances in Math., 236 (2013), 24--59.
(With A. J. Yee), Rogers-Ramanujan-Gordon Identities, generalized Gollnitz-Gordon identities and parity questions, J. Combin. Thy. Ser. (A) , 120 (2013), 1038--1056.
(With B. C. Berndt and A. Zaharescu), The circle and divisor problems, and Ramanujan's contributions through Bessel function series, The Legacy of Srinivasa Ramanujan: Proceedings of an International Conference in Celebration of the 125th Anniversary of Ramanujan's Birth: University of Delhi, 17--22 December 2012, B. C. Berndt and D. Prasad, eds., Ramanujan Mathematical Society, Mysore, 2013, pp. 111--127.
(With B. C. Berndt and A. Zaharescu), Weighted divisor sums and Bessel function series IV, Ramanujan J., 29 (2012), 79--102.
Exact covering systems in quadratic number fields, Quart. J. Math. (Oxford) , 63 No. 2 (2012), 165--180.
(With B. C. Berndt and A. Zaharescu), Weighted divisor sums and Bessel function series II, Advances in Math., 229 (2012), 2055--2097.
(With B. C. Berndt and C. Gugg), Ramanujan's elementary method in partition congruences, in Partitions, q-Series and Modular Forms, K. Alladi and F. Garvan, eds., Developments in Math. 23, Springer, New York, 2012, pp. 13--22.
(With A. J. Yee), Gollnitz-Gordon identities and parity questions, European J. of Combin., 32 (2011), 288--293.
A bijective proof of the quintuple product identity, International J. Number Thy., 6 No. 2 (2010), 247--256.
Bijective proofs of partition identities arising from modular equations, J. Combin. Thy. Ser. (A), 116 (2009), 699--712.
Covering systems in number fields, J. Number Thy., 129 (2009), 122--141.