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
- (with D. Prasad) Self-dual representations of division
algebras and Weil groups: A Contrast, with an appendix by D. Jiang and
D. Soudry, final version, to appear in the American Journal of
Mathematics, (2011).
Click for .pdf file of this paper.
- (with D. Prasad) On the cuspidality criterion for the Asai
transfer to
GL(4), to appear as an Appendix to a paper of M. Krishnamurthy,
(2011).
Click for .pdf file of this paper.
- An Exercise Concerning the Selfdual Cusp Forms on GL(3),
preprint (2009).
Click for pdf
file of this paper.
- A Mild Tchebotarev theorem for GL(n), preprint (2010).
Click for pdf file
of this paper
- Icosahedral fibres of the symmetric cube, preprint (2009),
to appear in the volume, On Certain L-functions, Proceedings of
a conference in honor of Freydoon Shahidi on his sixtieth birthday,
Clay Mathematics Proceeedings, American Math Society (2010).
Click for pdf file of this
paper
- (with K. Paranjape) Modular
forms and Calabi-Yau varieties, preprint (2008), being expanded
and revised.
Click for pdf file of this paper
- Remarks on the symmetric powers of cusp forms on GL (2), in
"Automorphic Forms and L-Functions: Global Aspects," Proceedings in
honor of Steve Gelbart on the occasion of his sixtieth birthday, ed. by
Ginzburg, Lapid and Soudry, pp. 237-256, AMS (2009)
Click for pdf file of this paper
- (with
Jacob Murre) Local Galois Symbols on ExE, dedicated to Spencer
Bloch, appears in Motives and Algebraic
Cycles: A Celebration in honour of Spencer J. Bloch, Fields Institute Communications, Volume 56
(2009)
Click for pdf file of 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, to appear in the American Journal of Mathematics
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
An+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:
Fall 2009
Spring 2010
Fall 2010
Fall 2011
Notes:
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
