(Last updated May 2009)
Office: Room # 216, Hill Center, Busch Campus
Email: rmunshi “at” math.rutgers.edu
Office Hour:
Address:
Department of Mathematics, Hill Center
110 Frelinghuysen Road
Piscataway NJ 08854
Research:
Papers:
1.
On effective determination of modular forms by twists
of critical L-values. (2009) (Submitted)
2.
On mean values and nonvanishing of derivatives of
L-functions in a nonlinear family. (2009) (Submitted)
3.
On the number of squares represented by a product of
two ternary quadratic forms. (2008) (To appear in The Quarterly Journal of
Mathematics)
4.
The circle method and pairs of quadratic forms. (Joint
with Iwaniec) (2008) (To appear in the Journal de Theorie des Nombres)
5.
Density of rational points on cyclic covers of P^n.
(Journal de Theorie des Nombres 21 no.2 (2009) 335-341.)
6.
Density of positive rank fibers in elliptic fibrations
-II. (2007) (To appear in the International Journal of Number Theory)
7.
The level of distribution of the special values of
L-functions. (2007) (To appear in Acta Arithmetica)
8.
Cubic polynomials and quadratic forms. (Joint with
Iwaniec) (2006-2007) (To appear)
9.
Density of rational points on elliptic fibrations -II.
(Acta Arithmetica 134 (2008), 133-140.)
10.
Density of rational points on elliptic fibrations. (Acta Arithmetica 129
(2007), 63-70.)
11.
Density
of positive rank fibers in elliptic fibrations. (Journal of Number Theory
125 (2007), 254-266.)
12.
Hilbert’s Nullstellensatz. (Bulletin of BMC (1999))
(See J.P. May’s article “Munshi’s
proof of the Nullstellensatz” Amer. Math. Monthly
110 (2003), no. 2, 133--140)
(See R.G. Swan’s article “On Munshi’s proof of the
Nullstellensatz”)
13.
Jordan curve theorem. (Part I) (Resonance 4 (1999) no. 9, 32-37)
14.
Jordan curve theorem. (Part II) (Resonance 4 (1999) no. 11, 14-20)
Preprints / work in progress:
1.
Integer solutions of y2 = u4 + v4
– w4. (2009) (Work in progress)
2.
On the weighted mean values of L-functions.
3.
Twisted Rankin-Selberg integrals.
4.
On analytic continuation of Dirichlet series.
Dissertation: The Arithmetic of Elliptic
Fibrations. (2006) Princeton University.
Teaching Spring 2009:
(1) Cryptography 640:348:01
Teaching Fall 2008:
(1)
Introductory
Linear Algebra: 640:250
(2)
Theory
of Numbers: 640:356
Teaching Spring 2008:
(1) Introductory Linear Algebra: 640:250
Teaching Fall 2007:
(1) Introductory Linear Algebra: 640:250 (Two sections)
Teaching Spring 2007:
(1)
Cryptography
640:348
Teaching Fall 2006:
(1) Introductory Linear Algebra: 640:250
(2) Advanced Calculus I: 640:311