School of Mathematics, Tata Institute of Fundamental Research
(last updated: July 30, 2015)
A case of simultaneous non-vanishing
(with J. Sengupta)
Hybrid subconvexity bounds for L(1/2, Sym^2 f x g)
(with R. Holowinsky and Z. Qi)
The circle method and bounds for $L$-functions – IV: Subconvexity for twists of GL(3) $L$-functions.
Annals of Math., to appear
Character sums of composite moduli and hybrid subconvexity
(with R. Holowinsky and Z. Qi). Contemp. Math., to appear
Pairs of quadrics in 11 variables.
Compositio Math., 151 (2015) 1189-1214
The circle method and bounds for $L$-functions - III: $t$-aspect subconvexity for GL(3) $L$-functions.
J. Amer. Math. Soc., 28 (2015) 913-938
The circle method and bounds for $L$-functions - II: Subconvexity for twists of GL(3) $L$-functions.
American J. Math. 137 (2015) 791-812
On some recent applications of circle method.
Math. Student 84 (2015) 23-38
Determination of GL(3) Hecke-Maass forms from twisted central values (with J. Sengupta).
J. Number Theory 148 (2015) 272-287
Pairs of diagonal quadratic forms and linear correlations among sums of two squares
(with Tim Browning) Forum Math. 27 (2015) 2025-2050
On effective determination of Maass forms from central values of Rankin-Selberg L-functions.
(with Jyoti Sengupta) Forum Math. 27 (2015) 467-488
The circle method and bounds for L-functions – I.
Math. Annalen 358 (2014) 389-401
Bounds for twisted symmetric square L-functions - III.
Advances in Math. 235 (2013) 74-91
Shifted convolution sums for GL(3) x GL(2).
Duke Math J. 162 (2013) 2345-2362
Shifted convolution of divisor function $d_3$ and the Ramanujan $\tau$ function.
The Legacy of Srinivasa Ramanujan, Ramanujan Math. Soc. Lec. Notes Ser. 20 (2013) 251-260
Bounds for twisted symmetric square L-functions – II. (unpublished)
Bounds for twisted symmetric square L-functions.
Journal für die reine und angewandte Mathematik (Crelle's Journal) 682 (2013) 65–88.
Rational points on singular intersections of quadrics.
(with Tim Browning) Compositio Math. 149 Issue 09 (2013), 1457 – 1494
A note on simultaneous nonvanishing twists.
Journal of Number Theory 132 (2012), no.4, 666-674
Level aspect subconvexity for Rankin-Selberg L-function.
(with Roman Holowinsky) International Colloquium on Automorphic Representations and L-functions, TIFR, 2012.
On a hybrid bound for twisted L-values.
Archiv der Math. 96 (2011), 3, 235-245
Inequalities for the divisor function.
The Ramanujan Journal 25 (2011), no. 2, 195-201
On quadratic families of CM elliptic curves.
Trans. Amer. Math. Soc. 363 (2011), 4337-4358.
On mean values and nonvanishing of L-functions in a nonlinear family.
Compositio Math. 147 (2011), 19-34
On the number of squares represented by a product of two ternary quadratic forms.
Q. J. Math 62 (2011), 157-171
On effective determination of modular forms by twists of critical L-values.
Math. Annalen 347, no. 4 (2010) 963-978
The circle method and pairs of quadratic forms. (with Henryk Iwaniec)
Journal de Theorie des Nombres de Bordeaux 22 no. 2 (2010) 403-419
Cubic polynomials and quadratic forms. (with Henryk Iwaniec)
Journal of the London Mathematical Society 81 (2010) 45-64
Density of positive rank fibers in an elliptic fibration -- II.
International Journal of Number Theory 6, no. 1, (2010) 15-23
Level of distribution of special values of L-functions.
Acta Arithmetica 138, no. 3 (2009)
Density of rational points on cyclic covers of P^n.
Journal de Theorie des Nombres de Bordeaux 21, no. 2 (2009), the special issue on 25th Journees Arithmetiques
Density of rational points on elliptic fibrations -- II.
Acta Arithmetica 134, no. 2 (2008)
Density of rational points on elliptic fibrations.
Acta Arithmetica 129, no. 1 (2007)
Density of positive rank fibers in an elliptic fibration.
Journal of Number Theory 125, no. 1 (2007)
The Jordan curve theorem.
Resonance No.9 September (1999), 32-37, No.11 November (1999), 14-20
Hilbert's Nullstellensatz, Bulletin of the Bombay Mathematical Colloquium, vol. 15, No. 1-2, January (1999), 20-24.
(See Prof. J.P. May's article "Munshi's Proof of the Nullstellensatz", Amer. Math. Monthly, 110 (2003), No. 2, 133--140; and Prof. R.G. Swan's article "On Munshi's Proof of the Nullstellensatz", http://www.math.uchicago.edu/~swan/nss.pdf)