There is a single light of science and to brighten it anywhere is to brighten it everywhere. - Isaac Asimov
Research
I was originally interested in analytic number theory, the Riemann zeta-function, and analytic combinatorics. Now I have extended my work to quantum computing and related topics. Here's a list of recent articles and some of my most immediate projects.
RAND MANUSCRIPTS (2023 - )
(28) The Riemann zeta function and exact exponential sum identities of divisor functions
joint work with M. Nastasescu, B. Stoica and A. Zaharescu
Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2024.128827)
(27) Exponential sums over Möbius convolutions with applications to partitions
joint work with D. Basak and A. Zaharescu
To appear in Canadian Journal of Mathematics (arXiv:2312.17435)
(26) Strange and pseudo-differentiable functions with applications to prime partitions
joint work with A. Dong, A. Zaharescu and D. Zeindler
Submitted (manuscript)
(25) Exponential sums twisted by general arithmetic functions
joint work with A. Dong, A. Zaharescu and D. Zeindler
Submitted (manuscript)
(24) Efficient quantum loading of probability distributions through Feynman propagators
joint work with E. Alhajjar, J. Geneson and A. Prakash
Submitted (arXiv:2311.13702)
(23) Estimating systemic importance with missing data in input-output graphs
joint work with J. Geneson, A. Moon, A. Strong and J. Welburn
Submitted (arXiv: 2310.02394)
IBM PAPERS (2021 - 2023)
(22) Partitions into semiprimes
joint work with M. Das, A. Zaharescu and D. Zeindler
Submitted (arXiv: 2212.12489)
(21) Partitions with multiplicities associated with divisor functions
joint work with B. C. Berndt, A. Zaharescu and D. Zeindler
Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2023.127987)
(20) Conditional Generative Models for Learning Stochastic Processes
joint work with S. Certo, A. Pham and A. Vlasic
Quantum Machine Intelligence (10.1007/s42484-023-00129-w)
(19) Expressivity of Variational Quantum Machine Learning on the Boolean Cube
joint work with D. Herman, R. Raymond, M. Li, A. Mezzacapo and M. Pistoia
IEEE Transactions on Quantum Engineering (10.1109/TQE.2023.3255206)
(18) A variational quantum algorithm for the Feynman-Kac formula
joint work with H. Alghassi, A. Deshmukh, N. Ibrahim, S. Woerner and C. Zoufal
Quantum (10.22331/q-2022-06-07-730)
ILLINOIS POSTDOCTORAL PUBLICATIONS (2015 - 2018)
(17) Breaking the ½ barrier for the twisted second moment of Dirichlet L-functions
joint work with H. M. Bui, K. Pratt and A. Zaharescu
Advances in Mathematics (10.1016/j.aim.2020.107175)
(16) Unexpected average values of generalized von Mangoldt functions in residue classes
joint work with A. Roy
Journal of the Australian Mathematical Society (10.1017/S1446788719000715)
(15) Random permutations with logarithmic cycle weights
joint work with D. Zeindler
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques (10.1214/19-AIHP1025)
(14) More than five-twelfths of the zeros of ζ are on the critical line
joint work with K. Pratt, A. Zaharescu and D. Zeindler
Research in the Mathematical Sciences (10.1007/s40687-019-0199-8)
(13) On mean values of mollifiers and L-functions associated to primitive cusp forms
joint work with P. Kühn and D. Zeindler
Mathematische Zeitschrift (10.1007/s00209-018-2099-9)
(12) Perturbed moments and a longer mollifier for critical zeros of ζ
joint work with K. Pratt
Research in Number Theory (10.1007/s40993-018-0103-4)
(11) Zeros of normalized combinations of ξ^{(k)}(s) on Re(s) = ½
joint work with S. Chaubey, A. Malik and A. Zaharescu
Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2017.12.045)
(10) Polynomial partition asymptotics
joint work with A. Dunn
Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2017.10.051)
(9) The largest gap between zeros of general L-functions is less than 41.54
joint work with P. Kühn and A. Zaharescu
Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2015.11.007)
(8) On a mollifier of the perturbed Riemann zeta-function
joint work with P. Kühn and D. Zeindler
Journal of Number Theory (10.1016/j.jnt.2016.09.022)
(7) Moments of averages of generalized Ramanujan sums
joint work with A. Roy
Monatshefte für Mathematik (10.1007/s00605-016-0907-z)
ZURICH DOCTORAL ARTICLES (2011 - 2015)
(6) Koshliakov kernel and identities involving the Riemann zeta function
joint work with A. Dixit, A. Roy and A. Zaharescu
Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2015.11.007)
(5) Twisted second moments of the Riemann zeta-function and applications
joint work with A. Roy and A. Zaharescu
Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2015.08.064)
(4) Explicit formulas of a generalized Ramanujan sum
joint work with P. Kühn
International Journal of Number Theory (10.1142/S1793042116500238)
(3) Zeros of combinations of the Riemann ξ-function on bounded vertical shifts
joint work with A. Dixit, A. Roy and A. Zaharescu
Journal of Number Theory (10.1016/j.jnt.2014.10.004)
(2) Zeta functions on tori using contour integration
joint work with E. Elizalde, K. Kirsten and F. L. Williams
International Journal of Geometric Methods in Modern Physics (10.1142/S021988781550019X)
(1) On a class of functions that satisfies explicit formulae involving the Möbius function
joint work with P. Kühn and A. Roy
The Ramanujan Journal (10.1007/s11139-014-9608-1)