Research Interests:  

    Number Theory, L-functions, Analytic problems for elliptic curves, Polynomials over finite fields.

  Publications

• Constants for Artin-like problems in Kummer and division fields (with Milad Fakhari), submitted, 20 pages.
  
• Value-Distribution of logarithmic derivatives of quadratic twists of automorphic $L$-functions (with Alia Hamieh), submitted, 33 pages.
  
• Fourier coefficients of automorphic L-functions over primes in ray classes (with P.-J. Wong),  submitted, 17 pages.
• Bounds for order of zeros of a class of Eisenstein series and their applications on dual pair of eta quotients (with Z. S. Aygin), Proceedings of the American Mathematical Society, 13 pages.
  
• Ambiguous solutions of a Pell equation (with F.J. Francis), Involve, 16 (2023), 13-25.
  
• Sums of triangular numbers and sums of squares (with Z. S. Aygin), Journal of Mathematical Analysis and Applications, 517 (2023), 26 pages.
  
• Two dimensional value-distribution of cubic Hecke L-functions (with A. Hamieh), Proceedings of the American Mathematical Society, 149 (2021), 4669-4684.
  
• On the moments of torsion points modulo primes and their applications (with P.-J. Wong), International Journal of Number Theory, 17 (2021), 1029-1045.
  
• Euler's function on products of primes in progressions (with F. J. Francis), Mathematics of Computation, 89 (2020), 993-1026.
  
• Value distribution of cubic Hecke L-functions (with A. Hamieh), Journal of Number Theory, 206 (2020), 81-122.
• On the Lang-Trotter conjecture for two elliptic curves (with J. Parks), Ramanujan Journal, 49 (2019), 585-623.
• On the average value of a function of the residual index (with A. T. Felix), GANITA, Springer Proc. Math. Stat., 251 (2018), 19-37.
  
• The largest known Wieferich numbers (with S. Siavashi), Integers, 18 (2018) #A3, 5 pages.
  
• The signs in elliptic nets (with M. Kumar and S. Yazdani), New York Journal of Mathematics, 23 (2017), 1237-1264.
  
• On the greatest prime factor of some divisibility sequences (with S. Yazdani), Contemporary Mathematics, 655, Centre Rech. Math. Proc. (volume in honor of 60th birthday of M. Ram Murty), 2015.
  
• On symmetries of elliptic nets and valuations of net polynomials (with J. Bleaney and S. Yazdani), Journal of Number Theory, 158 (2016), 185-216.
  
• On invariants of elliptic curves on average (with A. T. Felix), Acta Arithmetica, 168 (2015), 31-70.
• A log-free zero-density estimate and small gaps in coefficients of L-functions (with T. S. Trudgian), International Mathematics Research Notices, link.
  
• Limiting distributions of the classical error terms of prime number theory (with N. Ng and M. Shahabi), Quarterly Journal of Mathematics, link.
  
• A variant of the Bombieri-Vinogradov theorem with explicit constants and applications (with K. Hambrook), Mathematics of Computation (Electronically published in December 2014), link.
• Artin prime producing polynomials (with K. Scholten), Mathematics of Computation (Electronically Published in December 2014), link. Database.
  
• A geometric variant of Titchmarsh divisor problem (with D. Ghioca), International Journal of Number Theory, 8 (1) (2012), 53-69.
  
• Lower bounds for power moments of L-functions (with B. Fodden), Acta Arithmetica, 151 (2012), 11-38.
  
• On constructing permutations of finite fields (with D. Ghioca and Q. Wang), Finite Fields and Their Applications, 17 (2011), 51-67.
  
• Reductions of points on elliptic curves (with D. Ghioca and K. Murty), Mathematische Annalen, 347 (2010), 365-394.
  
• An analogue of the Siegel-Walfisz theorem for the cyclicity of CM wlliptic curves mod p (with K. Murty), Indian Journal of Pure and Applied Mathematics, 41 (1) (2010), 25-37.
  
• 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


• Analytic problems for number fields and elliptic curves, WAMS Research School in "Topics in Analytic and Transcendental Number Theory", Zanjan, Iran, July 2017.
  
• 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.