Ritabrata Munshi

Hill Assistant Professor

 

(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