Research Interests:  

    Number Theory, L-functions, Reduction mod p of  elliptic curves, Polynomials over finite fields.

  Publications:

• An analogue of the Siegel-Walfisz theorem for the cyclicity of CM wlliptic curves mod p (with K. Murty), to appear in Indian Journal of Pure and Applied Mathematics, 11 pages.
  
• Periods of orbits modulo primes (with D. Ghioca),  Journal of Number Theory, 129 (2009), 2831--2842.
  
• On permutation polynomials of prescribed shape (with D. Ghioca and Q. Wang),  Finite Fields and Their Application, 15 (2009), 195-206.
  
• On the greatest prime divisor of N_p, J. Ramanujan Math. Soc.,  23 (3)  (2008),  259-282.
• Superabundant numbers and the Riemann hypothesis (with Z. Friggstad), The American Mathematical Monthly, 116 (3) (2009), 273-275 .
• Reduction  mod p of subgroups of the Mordell-Weil group of an elliptic curve (with  K. Murty),  International  Journal of Number Theory, 5 (3)(2009), 465-487.
  
• On polynomials of the form x^r f(x^{(q-1)/l}) (with Q. Wang),  International Journal of Mathematics and Mathematical Sciences, 2007, Article ID 23408, 7 pages.
  
• Uniform distribution of zeros of Dirichlet series (with R. Murty),  The Anatomy of Integers, CRM, Montreal, 2008, 143-158.
  
• Explicit upper bounds for \prod_{p\leq p_\omega(n)} \frac{p}{p-1} (with Z. Friggstad and R. Juricevic), Contributions to Discrete Mathematics, 2 (2)(2007), 153-160.
  
• On some classes of permutation polynomials (with S. Alaric and Q. Wang),  International Journal of Number Theory, 4 (1)(2008), 121-133.
  
• On L^{r+1}(\pi,1/2),  C. R. Math. Rep. Acad. Sci. Canada,  28 (2) (2006), 33-38.
  
• Simultaneous non-vanishing of twists,  Proceeding of the American Mathematical Society, 134 (11) (2006), 3143-3151.
• A generalized Lucas sequence and permutation  binomials (with Q. Wang),  Proceeding of the American Mathematical Society,  134 (1) (2006), 15-22. 
• On some permutation polynomials over finite fields (with Q. Wang),  International Journal of Mathematics and Mathematical Sciences,  2005:16 (2005), 2631-2640.
  
• On non-vanishing of convolution of Dirichlet series (with S. Shahabi),  Canadian Mathematical  Bulletin, 48 (3) (2005), 321-332. 
• On non-vanishing of symmetric  square L-functions (with S. Shahabi),  Intern. Math. Journal, 5 (2) (2004), 169-181. 
• Average distributions and product of special values of L-series (with  C. David and R. Juricevic),  Acta  Arithmetica, 111 (2004), 239-268.
• Descending rational points on elliptic curves to smaller fields (with K. Murty),  Canadian  Journal of Mathematics,   53 (3) (2001),  449-469.
• Average values of symmetric square  L-functions at Re(s)=2, C. R. Math. Rep. Acad. Sci. Canada,  22 (3) (2000),   97-104.
• Non-vanishing of modular L-functions on a disc,  Acta  Arithmetica,  92  (2000), 303-318.
• Non-vanishing of  weight  k  modular L-functions with large level,  J.  Ramanujan  Math.  Soc.,  14 (1999),  37-54.
 
Lecture Notes


• Lectures on classical analytic theory of L-functions, IPM, Tehran, Iran, May 2006.
  

Thesis


• Non-vanishing of modular L-functions with large level,  Ph. D.  thesis, Dept. of Math.,  University of Toronto, 1997,  Under direction of   V.  K. Murty.
• Algebraic curves and Luroth semi-group, M. Sc.  thesis, Dept. of Math. and Computer Science, University of Tehran, 1991,  Under direction  of  R.  Zaare-Nahandi.