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 - )
(26) Exponential sums over Möbius convolutions with applications to partitions
joint work with D. Basak and A. Zaharescu
Submitted (arXiv:2312.17435)
(25) Efficient quantum loading of probability distributions through Feynman propagators
joint work with E. Alhajjar, J. Geneson and A. Prakash
Submitted (arXiv:2311.13702)
(24) The Riemann zeta function and exact exponential sum identities of divisor functions
joint work with M. Nastasescu, B. Stoica and A. Zaharescu
Submitted (arXiv: 2311.07657)
(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)