Taussky-Todd-Lonergan Professor of Mathematics

California Institute of Technology

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

Number theory, Automorphic forms, Arithmetic geometry, Representations of Lie and p-adic groups

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

*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*, preprint (2018), pp. 1-17.

elliptic curves

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*, Contemporary Math., Special volume in honor of J. Cogdell (2015), pp. 1-12.

degree one primes

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,(In memory of Serge Lang), 437–459,

Number theory, analysis and geometry*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., 13,2011

Amer. Math. Soc., Providence, RI,

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.*

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, 1998Click 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:

Fall 2010 Spring 2010

**Topics in Number Theory****Ma1c Analytical**

Fall 2009

LECTURE NOTES:

- Calculus
- Introduction to Number Theory
- Vector Calculus
- Modular forms over CM fields
- Differential Equations

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