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 Anna Szumowicz Xinwen Zhu Ashay Burungale
Courses taught during 2019-20:
Fall 2019
Freshman Math - Math 1a
Graduate Algebra - Math 120a
Selected Publications
- My Unforgettable Early Years at the IAS
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- Briggs-Haldane and Beyond:A Geometric View, Part I
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- Diophantine Equations: An Introduction
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- A theorem on GL(n) a la Tchebotarev, revised version, preprint (2018), pp. 1-17.
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- (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.
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- 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.
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(December 16, 2014).
- (with M. Dimitrov) Arithmetic quotients of the complex ball and a conjecture of Lang, preprint (2015),
Documenta Mathematica.
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(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.
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2014).
- A Mild Tchebotarev theorem for GL(n), J. Number Theory (Rallis memorial issue) 146 (2015), 519–533.
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- 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.
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- (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)
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- (with D. Prasad) On the cuspidality criterion for the Asai
transfer to
GL(4), preprint (2011), Appendix to M.
Krishnamurthy,
J. Number Theory (2012).
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- An Exercise Concerning the Selfdual Cusp Forms on
GL(3), Indian J. Pure Appl. Math. 45 (2014), no. 5, 777–785.
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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)
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- 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
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paper
- (with Nathan Dunfield) Increasing the number of fibered
faces of arithmetic hyperbolic 3-manifolds, Amer. J. Math. 132 , no. 1, 53–97 (2010)
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- 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)
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- (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)
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- Irreducibility and cuspidality. Representation theory and automorphic forms, 1–27, Progr. Math., 255, Birkhäuser Boston, Boston, MA, (2008)
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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)
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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)
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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)
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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).
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- (with J. Murre) Galois symbols on the square of an elliptic
curve, preprint
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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)
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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)
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- 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)
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- (with Song Wang) On the exceptional zeros of Rankin-Selberg
L-functions. Compositio Math. 135, no. 2, 211–244 (2003)
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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)
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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)
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- Expository talk at the IAS on Siegel zeros
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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)
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- 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)
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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
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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)
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- (with W. Luo) Determination of modular forms by
twists of critical L-values. Invent. Math. 130, no. 2, 371–398 (1997)
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- On the coefficients of cusp forms. Math. Res. Lett. 4, no. 2-3, 295–307 (1997)
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- (with J. Hoffstein) Siegel zeros and cusp forms. Internat. Math. Res. Notices 1995, no. 6, 279–308.
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Courses taught in earlier years: