## 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) 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)

(25) 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)

(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)