DINAKAR RAMAKRISHNAN
Taussky-Todd-Lonergan Professor of Mathematics
California Institute of Technology

Ph.D., Columbia University, N.Y., 1980

Research Interests

Number theory, automorphic forms, algebraic geometry, representations of Lie and p-adic groups

People at Caltech in Related Areas

• Elena Mantovan
• Tom Graber
• Matthias Flach

Selected Publications

• An Exercise Concerning the Selfdual Cusp Forms on GL(3), Preprint (2009).
  Click for pdf file of this paper.
• Remarks on the symmetric powers of cusp forms on GL (2), in "Automorphic Forms and L-functions", Volume, in honor of Steve Gelbert, edited by D. Ginzberg, E. Lapid and D. Soudry, Isreal Math conference Proceedings to appear (2008).
  Click for pdf file of this paper.
• (with Jacob Murre) Local Galois Symbols on ExE, dedicated to Spencer Bloch, Preprint (2008).
  Click for pdf file of this paper.
• (with Philippe Michel) Consequences of the Gross-Zagier formulae: Stability of average L-values, subconvexity, and non-vanishing mod p, In memory of Serge Lang, Preprint (2007).
  Click for pdf file of this paper.
• (with Nathan Dunfield) Increasing the number of fibered faces of arithmetic hyperbolic 3-manifolds.
  Click for pdf file of this paper.
• (with D. Prasad) Self-dual representations of division algebrasand Weil groups: A Contrast, Preprint (2008).
  Click for .pdf file of this paper.
• (with F. Shahidi) Siegel modular forms of genus 2 attached to elliptic curves, Math Research Letters 14, no. 2, 315--332, (2007).
  Click for .pdf file of this paper.
• Irreducibility and cuspidality, in Representation Theory and Automorphic Forms, Progress in Math., Volume 255, Birkhäuser, 1-27 (2008).
  Click for .pdf file of this paper.
• Modular curves, modular surfaces and modular fourfolds, in Algebraic Cycles and Motives, Volume 1, 278-292, dedicated to Jacob Murre, Cambridge University Press, London Math. Soc. Lecture Notes 343  (2007).
  Click for .pdf file of this paper.
• (with J. Rogawski) Average values of modular L-series via the relative trace formula, Pure and Applied Mathematics Quarterly 1, No.4, 701-735 (2005) - In memory of Armand Borel.
  Click for .pdf file of this paper.
• (with K. Paranjape) Quotients of Eⁿ by A_n+1 and Calabi-Yau manifolds, Algebra and Number Theory, 90–98, Hindustan Book Agency, Delhi (2005).
  Click for .ps file or .pdf file or .dvi file of this paper.
• (with J. Murre) Galois symbols on the square of an elliptic curve, Preprint.
  Click for ps file or .pdf file or .dvi file of an abstract of this paper. 
• (with S. Wang) A cuspidality criterion for the functorial product on GL(2) × GL (3), with a cohomological application, IMRN 2004, No. 27, 1355-1394.
  Click for .ps file or .pdf file or .dvi file of this paper
• Algebraic cycles on Hilbert modular fourfolds and poles of L-functions, Proceedings of the International Conference on Algebraic Groups and Arithmetic, 271-274 (2005).
  Click for .ps file or .pdf file or .dvi file of this paper
• Existence of Ramanujan primes for GL(3), in "Contributions to Automorphic Forms, Geometry, and Number Theory," 711-717, JHU Press, Baltimore (2004).
  Click for .ps file or .pdf file or .dvi file of this paper
• (with Song Wang) On the exceptional zeros of Rankin-Selberg L-functions, to appear in Compositio Mathematica 135 (2003), 211-244.
  Click for .ps file or .pdf file or .dvi file of this paper.
• A descent criterion for isobaric representations, appendix to "Functoriality for the exterior square of GL₄ and the symmetric fourth of GL₂" by H.Kim, J. Amer. Math. Soc. 16 (2003), no. 1, 139-183.
  Click for .ps file or .pdf file or .dvi file of this paper
• Modularity of solvable Artin representations of GO(4)-type, IMRN 2002, No. 1, 1-54.
  Click for .ps file or .pdf file or .dvi file of this paper
• Expository talk at the IAS on Siegel zeros.
  Click for .ps file or .pdf file or .dvi file of this paper
• (with Robert Valenza) Fourier Analysis on Number Fields, Springer-Verlag, Berlin (1998).
  For information about this book, click here. For reviews, click here and here.
• Modularity of the Rankin-Selberg L-series, and multiplicity one for SL(2), Annals of Math. 152 (2000), 45-111.
  Click for .ps file or .pdf file or .dvi file of this paper.
• (with W. Luo) Determination of modular elliptic curves by Heegner points, Pacific J. Math., Olga Taussky-Todd Memorial Issue, 1998.
  Click for .ps file or .pdf file or .dvi file of this paper.
• (with D. Prasad) On the global root numbers of GL(n) × GL(m), in "Automorphic Forms, Automorphic Representations, and Arithmetic," part 2, pp. 311–330, Proceedings of the Symposia in Pure Math., vol. 66, AMS (1999).
  Click for .ps file or .pdf file or .dvi file of this paper.
• (with W. Luo) Determination of modular forms by twists of critical L-values, Invent. Math. 130 (1997), 371-398.
  Click for .ps file or .pdf file or .dvi file of this paper.
• On the coefficients of cusp forms, Math. Research Lett. 4 (1997), 295-307.
  Click for .ps file or .pdf file or .dvi file of this paper.
• Recovering modular forms from squares, appendix to: "A problem of Linnik and mean value estimates for automorphic representations" by Duke and Kowalski, Invent. Math. 139 (2000), 29-39.
  Click for .ps file or .pdf file or .dvi file of this paper.

Courses taught during Spring 2007:

Topics in Number Theory

Ma1c Analytical

Notes:

• Calculus
• Introduction to Number Theory
• Vector Calculus
• Modular forms over CM fields

Personal Information

• Married to Mary Patricia Carlton
• Son: Anand Ramakrishnan (born on October 24, 1993)

Go to the Directory for mailing address, fax and telephone numbers, and e-mail address.

Click here to get a listing of D. Ramakrishnan's papers from the AMS MathSciNet with links to Mathematical Reviews.
(Note: You or your institution must have a valid MathSciNet subscription.)

Math Department Home Page