Published papers and Preprints

  1. Zeros of partial sums of $L$-functions (with Akshaa Vatwani), preprint.
  2.  
  3. Unnormalized differences of the zeros of the derivative of the completed $L$-function, preprint.
  4.  
  5. On the distribution of zeros of derivatives of the Riemann $\xi$-function (with A. Malik), submitted.
  6.  
  7. On a generalization of the Selberg formula, Siegel zero and the Weil explicit formula (with N. M. Robles), to appear in Acta Arith.
  8.  
  9. Moments of averages of generalized Ramanujan sums (with N. M. Robles), Monatsh. Math. 182 (2017), no. 2, 433-461.
  10.  
  11. Smooth $L^2$ Distances and Zeros of Approximations of Dedekind zeta functions (with J. Li, M. Nastasescu, and A. Zaharescu), Manuscripta Math. 154 (2017), no. 1-2, 195-223.
  12.  
  13. Error functions, Mordell integrals and an integral analogue of partial theta function (with A. Dixit and A. Zaharescu), Acta Arith. 177 (2017), no. 1, 1-37.
  14.  
  15. New Pathways and Connections in Analysis and Analytic Number Theory Motivated by Two Incorrect Claims of Ramanujan (with B.C. Berndt, A. Dixit, and A. Zaharescu), Adv. Math. 304 (2017), 809-929.
  16.  
  17. Twisted second moments of the Riemann zeta-function and applications (with N. M. Robles and A. Zaharescu), J. Math. Anal. Appl. 434 (2016), no. 1, 271-314.
  18.  
  19. Koshliakov kernel and identities involving the Riemann zeta-function (with N. M. Robles, A. Dixit and A. Zaharescu), J. Math. Anal. Appl. 435 (2016) 1107-1128.
  20.  
  21. Zeros of a family of approximations of Hecke L-functions associated with cusp forms (with J. Li and A. Zaharescu), Ramanujan J. 41 (2016), no. 1-3, 391-419. pdf
  22.  
  23. Riesz-type criteria and theta transformation analogues (with A. Dixit and A. Zaharescu), J. Number Theory 160 (2016), 385-408.
  24.  
  25. Some identities involving convolutions of Dirichlet characters and the Möbius function (with A. Zaharescu and M. Zaki),Proc. Indian Acad. Sci. Math. Sci. 126 (2016), no. 1, 21-33. Sci. Math. Sci.. pdf
  26.  
  27. Ramanujan-Hardy-Littlewood-Riesz Type phenomena for Hecke forms (with A. Dixit and A. Zaharescu), J. Math. Anal. Appl., 426 No 1, (2015), 594-611.
  28.  
  29. Zeros of combinations of the Riemann $\xi$-functions on bounded vertical shifts (with A. Dixit, N. Robles and A. Zaharescu), Journal of Number Theory, 149 (2015), 404 - 434 .
  30.  
  31. On a class of functions that satisfies Ramanujan's explicit formula (with P. Kühn and N. Robles),Ramanujan J. 38 (2015), no. 2, 383-422.
  32.  
  33. Zeros of partial sums of the Dedekind zeta function of a cyclotomic field ( with A. Ledoan and A. Zaharescu), J. Number Theory, 136 (2014), 118-133. pdf
  34.  
  35. Monotonicity Results for Dirichlet L-Functions (with A. Dixit and A. Zaharescu), J.Math.Anal.Appl., 410 No 1, (2014), 307-315., pdf
  36.  
  37. Sums of magnetic eigenvalues are maximal on rotationally symmetric domains (with R. S. Laugesen and J. Liang), Annales Henri Poincarè., 13 (2012), 731-750., pdf
  38.  
  39. Convexity of quotients of theta functions (with A. Dixit and A. Zaharescu), J.Math.Anal.Appl., 386 No 1, (2012), 319-331., pdf