## DINAKAR RAMAKRISHNANTaussky-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

#### People at Caltech in Related Areas

• Elena Mantovan    Matthias Flach    Tom Graber    Xinwen Zhu     Zavosh Amir Khosravi

#### Courses taught during 2018-19:

• Freshman Math - Math 1a
• Graduate Algebra - Math 120a

#### Selected Publications

• 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.
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.
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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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• (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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• (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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• (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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• 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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• (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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• (with K. Paranjape) Quotients of En by An+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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• (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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• 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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• 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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• 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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• (with Robert Valenza) Fourier analysis on number fields. Graduate Texts in Mathematics, 186. Springer-Verlag, New York  (1999).
• 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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• (with W. Luo) Determination of modular elliptic curves by Heegner points, Pacific J. Math., Olga Taussky-Todd Memorial Issue, 1998
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• (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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