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, Arithmetic geometry,
Representations of Lie and p-adic groups, Mathematical Biology
People at Caltech in Related Areas
- Elena Mantovan Matthias Flach Tom Graber Xinwen Zhu Ashay Burungale
Courses taught during 2019-20:
Fall 2019
Freshman Math - Math 1a
Graduate Algebra - Math 120a
Selected Publications
- Briggs-Haldane and Beyond:A Geometric View, Part I
Click for pdf file of this paper.
- Diophantine Equations: An Introduction
Click for pdf file of this paper.
- A theorem on GL(n) a la Tchebotarev, revised version, preprint (2018), pp. 1-17.
Click for pdf file of this paper.
- (with D.R. Grayson Eisenstein series of weight one, q-averages of the 0-logarithm and periods of
elliptic curves, preprint (2018), pp. 1-17.
Click for pdf file of this paper.
- Base Change of Hecke Characters Revisited (2016), pp. 1-11. Click
for pdf file of this paper
- Recovering cusp forms on GL(2) from symmetric cubes, Contemporary Math.,
Special volume in honor of Ram Murty (2015), pp. 1-9. Click
for pdf file of this paper
- (with K. Martin) A Comparison of automorphic and Artin L-series of
GL(2)-type agreeing at
degree one primes, Contemporary Math., Special volume in honor of
J. Cogdell (2015), pp. 1-12.
Click for pdf file of this paper
(December 16, 2014).
- (with M. Dimitrov) Arithmetic quotients of the complex ball and a conjecture of Lang, preprint (2015),
Documenta Mathematica.
Click for pdf file of this paper
(December, 2015).
- (with K. Paranjape) Modular
forms and Calabi-Yau varieties, Arithmetic and geometry, 351–372, London Math. Soc. Lecture Note Ser. 420, Cambridge Univ. Press, Cambridge, 2015.
Click for pdf file of this paper (March 31,
2014).
- A Mild Tchebotarev theorem for GL(n), J. Number Theory (Rallis memorial issue) 146 (2015), 519–533.
Click for pdf file of this pape
- Decomposition and parity of Galois representations
attached to GL(4), Automorphic representations and L-functions, 427–454,
Tata Inst. Fundam. Res. Stud. Math., 22, Tata Inst. Fund. Res.,
Mumbai, 2013.
Click for pdf file of this paper.
- (with D. Prasad) Self-dual representations of division
algebras and Weil groups: A Contrast, with an appendix by D. Jiang and
D. Soudry, Amer. J. Math.
134 , no. 3, 729-742 (2012)
Click for .pdf file of this paper.
- (with D. Prasad) On the cuspidality criterion for the Asai
transfer to
GL(4), preprint (2011), Appendix to M.
Krishnamurthy,
J. Number Theory (2012).
Click for .pdf file of this paper.
- An Exercise Concerning the Selfdual Cusp Forms on
GL(3), Indian J. Pure Appl. Math. 45 (2014), no. 5, 777–785.
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,
Number theory, analysis and geometry (In memory of Serge Lang),
437–459, Springer, New York (2012)
Click for pdf file of this paper
- Icosahedral fibres of the symmetric cube and
algebraicity, On certain L-functions (In honor of Freydoon Shahidi), 483–499, Clay Math. Proc., 13,
Amer. Math. Soc., Providence, RI, 2011
Click for .pdf file of this
paper
- (with Nathan Dunfield) Increasing the number of fibered
faces of arithmetic hyperbolic 3-manifolds, Amer. J. Math. 132 , no. 1, 53–97 (2010)
Click for pdf file of this paper
- Remarks on the symmetric powers of cusp forms on GL(2), Automorphic forms and L-functions I. Global aspects (In honor of
Steve Gelbart), 237–256,
Contemp. Math., 488, Amer. Math. Soc., Providence, RI, 2009 (2009)
Click for pdf file of this paper
- (with Jacob Murre) Local Galois symbols on E x E, Motives and algebraic cycles, 257–291, Fields Inst. Commun., 56, Amer. Math. Soc., Providence, RI,(2009)
Click for pdf file of paper
- Irreducibility and cuspidality. Representation theory and automorphic forms, 1–27, Progr. Math., 255, Birkhäuser Boston, Boston, MA, (2008)
Click for .pdf
file of this paper.
- (with F. Shahidi) Siegel modular forms of genus 2
attached to elliptic curves. Math. Res. Lett. 14, no. 2, 315–332 (2007)
Click for .pdf
file of this paper.
- Modular curves, modular surfaces, and modular
fourfolds. Algebraic cycles and motives (dedicated to Jacob
Murre), Vol. 1, 278–292,
London Math. Soc. Lecture Note Ser., 343, Cambridge Univ. Press,
Cambridge (2007)
Click for .pdf
file of this paper.
- (with J. Rogawski) Average values of modular L-series via the relative trace formula, Pure Appl. Math. Q. 1, no. 4,
Special Issue: In memory of Armand Borel. Part 3, 701–735 (2005)
Click for .pdf
file of this paper.
- (with K. Paranjape) Quotients of E^{n} 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) x GL(3) with a cohomological application, Int. Math. Res. Not. no. 27, 1355–1394 (2004)
Click for .ps
file or .pdf
file or .dvi
file of this paper
- Algebraic cycles on Hilbert modular fourfolds and
poles of L-functions. Algebraic groups and arithmetic, 221–274, Tata Inst. Fund. Res., Mumbai (2005)
Click for .ps file or .pdf file or .dvi file
- Contributions to automorphic forms, geometry, and number theory (In honor of Joseph Shalika), 711–717, Johns Hopkins Univ. Press, Baltimore, MD (2004)
- 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. Compositio Math. 135, no. 2, 211–244 (2003)
Click for .ps
file or .pdf
file or .dvi
file of this paper
- A descent criterion for isobaric representations, Appendix I, "Functoriality for the exterior square of GL_4 and the symmetric fourth of GL_2" by H. Kim, J. Amer. Math. Soc.
16, no. 1, 171-175 (2003)
Click for .ps
file or .pdf
file or .dvi
file of this paper
- Modularity of solvable Artin representations of GO(4)-type. Int. Math. Res. Not., no. 1, 1–54 (2002)
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. Graduate Texts in Mathematics, 186. Springer-Verlag, New York (1999).
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), Ann. of Math. (2) 152, no. 1, 45–111 (2000)
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, 29-39 (2000)
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, no. 2, 371–398 (1997)
Click for .ps file or .pdf file or .dvi file of this paper.
- On the coefficients of cusp forms. Math. Res. Lett. 4, no. 2-3, 295–307 (1997)
Click for .ps file or .pdf file or .dvi file of this paper.
- (with J. Hoffstein) Siegel zeros and cusp forms. Internat. Math. Res. Notices 1995, no. 6, 279–308.
Click for .pdf file of this paper.
Courses taught in earlier years: