Research

I am interested in analytic number theory and the Riemann zeta-function. Here's a list of recent work and some of my most immediate projects.

POST-DOCTORAL PAPERS (2015-)

(14) Perturbed moments and a longer mollifier for critical zeros of ζ
joint work with K. Pratt
Submitted (arXiv: 1706.04593)

(13) Polynomial Partition Asymptotics
joint work with A. Dunn
Submitted (arXiv: 1705.00384)

(12) On a generalization of Selberg's formula, Siegel's zero, and Weil's formula
joint work with A. Roy
Submitted

(11) Zeros of normalized combinations of ξ(k)(s) on Re(s)=1/2
joint work with S. Chaubey, A. Malik and A. Zaharescu
Submitted

(10) On mean values for Dirichlet's polynomials and L-functions
joint work with P. Kühn and D. Zeindler
Submitted (arXiv: 1609.03738)

(9) The largest gap between zeros of entire 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.2016.12.007)

(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)

DOCTORAL PAPERS (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
Int. J. Geom. Methods Mod. Phys. (10.1142/S021988781550019X)

(1) On a class of functions that satisfies explicit formulae involving the μ function
joint work with P. Kühn and A. Roy
The Ramanujan Journal (10.1007/s11139-014-9608-1)

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