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Atul Dixit

Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street, Urbana, Illinois 61801.

Contact

Office: B4 A Coble Hall
Phone: (217)-244-1967
Email: aadixit2[at]illinois.edu

Biographical Information

Research Interests

I am primarily interested in Analytic number theory, q-series, Theory of Partitions and Special functions. I like to work in the areas of Mathematics developed by Srinivasa Ramanujan. This is my sixth year of PhD. My thesis advisor is Prof. Bruce C. Berndt. Here is my Curriculum Vitae.

Publications

  1. Orthopoles and the Pappus Theorem (with D. Grinberg), Forum Geom., 4, (2004), 53-59, (pdf).
  2. Monotonicity of quotients of theta functions related to an extremal problem on harmonic measure (with A. Yu. Solynin) J. Math. Anal. Appl., 336, No. 2, (2007), 1042-1053.
  3. The Laplace transform of the psi function, Proc. Amer. Math. Soc., 138, No. 2 (2010), 593-603.
  4. Series transformations and integrals involving the Riemann $Xi$-function, J. Math. Anal. Appl., 368, (2010), 358-373.
  5. A transformation formula involving the Gamma and Riemann zeta functions in Ramanujan's Lost Notebook (with B. C. Berndt), The legacy of Alladi Ramakrishnan in the mathematical sciences, K. Alladi, J. Klauder, C. R. Rao, Eds, Springer, New York, 2010, pp.199-210, (pdf).
  6. Character analogues of theorems of Ramanujan, Koshliakov and Guinand (with B. C. Berndt and J. Sohn), Adv. Appl. Math., 46, Issues 1-4, (2011), 54-70 (Special issue in honor of Dennis Stanton). (pdf).
  7. Analogues of a transformation formula of Ramanujan, Int. J. Number Theory, 7, No. 5 (2011), 1151-1172.
  8. Transformation formulas associated with integrals involving the Riemann $Xi$-function, Monatsh. Math., 164, No. 2, (2011), 133-156 (pdf).
  9. Convexity of quotients of theta functions (with A. Roy and A. Zaharescu), J. Math. Anal. Appl., 386, No. 1, (2012), 319-331 (pdf).
  10. Character analogues of Ramanujan type integrals involving the Riemann $\Xi$-function, to appear in Pacific Journal of Mathematics, (pdf).
  11. Rank-Crank type PDEs and generalized Lambert series identities (with S. H. Chan and F. G. Garvan), to appear in Ramanujan journal (Special issue in honor of Mourad Ismail and Dennis Stanton), (pdf).
  12. Analogues of the general theta transformation formula, submitted for publication, (pdf).
  13. Ramanujan-Hardy-Littlewood type results for primitive Hecke forms (with A. Roy and A. Zaharescu), in preparation.

Conference talks

  1. Monotonicity of Quotients of Theta Functions, Midwest Number Theory Conference for Graduate Students IV, University of Illinois at Urbana- Champaign, October 28-29, 2006.
  2. Generalizing Theorems of Ramanujan, Koshliakov and Guinand for even, periodic and completely multiplicative sequences, Illinois Number Theory Fest, Conference in the honor of 80th Birthday celebration of Heini Halberstam and John Selfridge, University of Illinois at Urbana-Champaign, May 16-20, 2007.
  3. Character Analogues of formulas of Ramanujan, Koshliakov and Guinand, Midwest Number Theory Conference for Graduate Students V, University of Wisconsin at Madison, November 3-4, 2007.
  4. A transformation formula involving the Gamma and Riemann zeta functions in Ramanujan's Lost Notebook, Combinatory Analysis 2008, Conference in the honor of George E. Andrews' 70th birthday, Penn State University, December 5-7, 2008.
  5. Analogues of a transformation formula of Ramanujan, Quadratic Forms, Sums of Squares, Theta Functions and Integral Lattices conference, University of Florida at Gainesville, March 11-15, 2009.
  6. Transformation formulas associated with integrals involving the Riemann $\Xi$ function, 2009 AMS Fall Central Sectional Meeting, Special Session on contemporary Complex and Special Function Theory, Baylor University, October 16-18, 2009.
  7. Transformation formulas associated with integrals involving the Riemann $\Xi$ function, Midwest Number Theory Conference for Graduate Students VI, University of Wisconsin at Madison, November 7-8, 2009.
  8. Transformation formulas associated with integrals involving the Riemann $\Xi$ function, Focused week on Quadratic Forms and Theta functions, University of Florida at Gainesville, March 22-26, 2010.
  9. Character analogues of Ramanujan type integrals involving the Riemann $\Xi$ function, Joint Mathematics Meeting, Special session on Asymptotic Methods in Analysis with Applications II, New Orleans, January 6-9, 2011.
  10. A hypergeometric proof of a Rank-Crank type PDE, q-series 2011 , q-series, partitions and special functions conference in the honor of Mourad Ismail and Dennis Stanton, Georgia Southern University , March 14-16, 2011.
  11. Rank-Crank type PDEs through the identities of Jackson and Chan, Midwest Number Theory conference for Graduate Students 2011, University of Wisconsin at Madison, November 18-20, 2011.

Expository Papers

  1. Fermatche Shevatche Prameya (in Marathi), English translation: 'Fermat's Last Theorem', December 26, 2004, (pdf).

Teaching

:This Spring I am teaching Math 234 (Section DL1) Calculus for Business I. My previous teaching assignments were as follows.

Links

  • Last updated on January 24, 2012.