## 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)