## 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)