| Generating cryptographically-strong random lattice bases and recognizing rotations of Zn, with Tamar Lichter Blanks, preprint. |
| A template method for Fourier coefficients of Langlands Eisenstein series, with Dorian Goldfeld and Michael Woodbury, to appear in Rivista di Matematica della Universita di Parma, Proceedings of the "Second Symposium on Analytic Number Theory". |
| On Arthur's unitarity conjecture for split real groups, with Joseph Hundley, preprint. |
| Stopping time signatures for some algorithms in cryptography, with Percy Deift and Thomas Trogdon, preprint. |
| Universal optimality of the E8 and Leech lattices and interpolation formulas , with Henry Cohn, Abhinav Kumar, Danylo Radchenko, and Maryna Viazovska, preprint. |
| On the nonexistence of automorphic eigenfunctions of exponential growth on SL(3,Z)\SL(3,R)/SO(3,R), with Tien D. Trinh, preprint. |
| Kissing numbers and transference theorems from generalized tail bounds, with Noah Stephens-Davidowitz, preprint. |
| Coppersmith's lattices and ``focus groups'': an attack on small-exponent RSA, with Bhargav Narayanan and Ramarathnam Venkatesan, Journal of Number Theory 222 (2021), pp. 376-392. |
| A Spectral reciprocity formula and non-vanishing for L-functions on GL(4)xGL(2), with Valentin Blomer and Xiaoqing Li, preprint. |
| Weights, raising and lowering operators, and K-types for automorphic forms on SL(3,R), with Jack Buttcane, to appear in Representation Theory, Complex Geometry, and Automorphic Forms, International Press. |
| The balanced Voronoi formulas for GL(n), with Fan Zhou, International Mathematics Research Notices 2019, pp. 3473-3484. |
| Estimates on Eisenstein distributions for reciprocals of p-adic L-functions: the case of irregular primes, with Stephen Gelbart, Ralph Greenberg, and Freydoon Shahidi, in Representation Theory, Number Theory, and Invariant Theory: In Honor of Roger Howe on the Occasion of His 70th Birthday, Ju-Lee Kim, James Cogdell, and Chengbo Zhu, editors, pp. 193-208, Progress in Mathematics 323, Birkhauser, 2017. |
| The sphere packing problem in dimension 24, with Henry Cohn, Abhinav Kumar, Danylo Radchenko, and Maryna Viazovska, Annals of Mathematics 185 (2017), 1017-1033. |
| Some properties of optimal functions for sphere packing in dimensions 8 and 24, with Henry Cohn, preprint. |
| On the nonexistence of automorphic eigenfunctions of exponential growth on SL(3,Z)\SL(3,R)/SO(3,R), with Tien D. Trinh, preprint. Video presentation. |
| Cryptanalysis of the NFL schedule (expository piece). |
| Non-abelian analogs of lattice rounding, with Evgeni Begelfor and Ramarathnam Venkatesan, Groups Complexity Cryptology 7 (2015), pp.117-133. |
| SL(2,Z)-invariance and D-instanton contributions to the D^6R^4 interaction, with Michael B. Green and Pierre Vanhove, Communications in Number Theory and Physics 9 (2015), pp.307-344. |
| Entirety of cuspidal Eisenstein series on loop groups, with Howard Garland and Manish Patnaik, American Journal of Mathematics, 139 (2017), pp. 461-512. |
| A p-adic integral for the reciprocal of L-functions, with Stephen Gelbart, Alexei Pantchichkine, and Freydoon Shahidi, in Automorphic forms and related geometry: assessing the legacy of I. I. Piatetski -Shapiro, pp.53-68, Contemp. Math., 614, Amer. Math. Soc., Providence, RI, 2014 |
| Residual automorphic forms and spherical unitary representations of exceptional groups, Annals of Mathematics. 177 (2013), pp. 1169-1179. Computer programs can be found here. |
| Small representations, string instantons, and Fourier modes of Eisenstein series, with Michael Green and Pierre Vanhove; includes appendix "Special unipotent representations" by Dan Ciubotaru and Peter E. Trapa, J. Number Theory 146 (2015), pp. 187-309. |
| Fourier coefficients of automorphic forms, character variety orbits, and small representations, with Siddhartha Sahi, Journal of Number Theory 132 (2012), pp. 3070-3108. |
| The archimedean theory of the Exterior Square L-functions over Q, with Wilfried Schmid, Journal of the American Mathematical Society 25 (2012), pp. 465-506. |
| Adelization of Automorphic Distributions and Mirabolic Eisenstein Series, with Wilfried Schmid, in Representation theory and mathematical physics, J. Adams, B. Lian, and S. Sahi, editors, Contemporary Mathematics 557 (2011), pp. 289-334. |
| Pairings of automorphic distributions, with Wilfried Schmid, Mathematische Annalen 353 (2012), pp. 581-597. |
| On the rapid decay of cuspidal automorphic forms, with Wilfried Schmid, Advances in Mathematics 231 (2012), 940-964. |
| Eisenstein series for higher-rank groups and string theory amplitudes, with Michael Green, Jorge Russo, and Pierre Vanhove, in Communications in Number Theory and Physics, Volume 4, No. 3, September 2010, pp. 551-596. |
| A general Voronoi summation formula for GL(n,Z), with Wilfried Schmid, in Geometric analysis: Present and Future, procedings of a conference held in honor of the 60th birthday of Shing-Tung Yau at Harvard, August 27-Sept 1, 2008 (in the Advanced Lectures in Math series of International Press). |
| Expander graphs based on GRH and an application to elliptic curve cryptography, with David Jao and Ramarathnam Venkatesan, Journal of Number Theory 129 (2009), pp. 1491-1504. |
| Non-degeneracy of Pollard Rho Collisions, with Ramarathnam Venkatesan, in International Mathematics Research Notices, 2009, pp.1-10. |
| A method for computing general automorphic forms on general groups, Forum Mathematicum, 22 (2010), pp.1207-1211. |
| Distinguishing attacks on stream ciphers based on arrays of pseudo-random words, with Nathan Keller, Information Processing Letters 110 (2010), pp. 129-132. |
| MV3: A new stream cipher based on random walks and revolving buffers, with Nathan Keller, Ilya Mironov, and Ramarathnam Venkatesan, Topics in Cryptology -- Procedings of CT-RSA 2007, Springer Verlag Lecture Notes in Computer Science, 4377 (2007), pp. 1-19. |
| Spectral
Analysis
of Pollard Rho Collisions, with Ramarathnam Venkatesan,
Procedings of the 7th Algorithmic
Number
Theory
Symposium (Berlin),
Springer-Verlag Lecture Notes in Computer Science 4076 (2006), pp.
573-581. |
| The
Rankin-Selberg method for
automorphic distributions, with Wilfried Schmid, Representation
Theory and
Automorphic Forms, Progress in Mathematics 255,
Birkhauser, Boston, 2008, pp.111-150. |
| Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log?, with David Jao and Ramarathnam Venkatesan, in Advances in Cryptology - ASIACRYPT 2005: 11th International Conference on the Theory and Application of Cryptology and Information Security, Springer Verlag Lecture Notes in Computer Science, 3788 (2005), pp. 21-40. |
|
Cancellation
in additively twisted sums on
GL(n), American
Journal of
Mathematics, 128
(2006), pp. 699-729.
|
|
The
Highly Oscillatory
Behavior of Automorphic Distributions for SL(2), with Wilfried
Schmid, Letters
in Mathematical Physics, 69 (2004),
265--286.
|
| Automorphic Distributions, L-functions, and Voronoi Summation for GL(3), with Wilfried Schmid, Annals of Mathematics 164 (2006), pp. 423-488. |
|
Distributions
and Analytic Continuation of Dirichlet Series, with Wilfried
Schmid, Journal of Functional Analysis, 214
(2004), pp.
155-220.
|
|
Summation
Formulas, from Poisson and Voronoi to the Present, with
Wilfried
Schmid, in Noncommutative Analysis, in Honor of Jacques
Carmona,
Progress in Mathematics 220 (2003), Birkhäuser, pp.
419-440.
(Includes a short explanation of the above two, longer
papers.)
|
| "Riemann's Zeta Function and Beyond," with Stephen Gelbart, Bulletin of the American Mathematical Society, 41, (2004), 59-112 |
| Non-vanishing of the central derivative of canonical Hecke L-functions, with Tonghai Yang, Math. Res. Letters, 7 (2000), pp. 263-278. |
|
The
Highest-Lowest
Zero and
other Applications of Positivity, Duke
Mathematical
Journal, Volume 112, No. 1, pp.83-116.
|
| On the Existence and
Temperedness of Cusp Forms for SL(3,Z), Journal
für
die reine und angewandte
Mathematik, 533 (2001), pp.
127-169. |
|
A simpler way to show
zeta(3) is
irrational PDF, Postscript, or DVI |
| Level
spacings for regular
graphs (with
D. Jakobson, I. Rivin, and Z. Rudnick), The IMA Volumes in Mathematics
and its Applications, Volume 109, "Emerging Applications of Number
Theory," Dennis Hejhal, Fan Chung, Joel Friedman, Martin Gutzwiller,
and Andrew
Odlyzko (eds.), Springer-Verlag New York, Inc. (1999), pp. 317-327. PDF or Postscript |
| Spectral
and Cohomological Applications of the Rankin-Selberg Method, International Mathematics Research Notices, 1996, No. 1, pp. 15-26. |