Stephen D. Miller

Professor of mathematics, Rutgers University

Research interests

Automorphic Forms
L-functions (See the Database of Automorphic L-functions)
Analytic Number Theory

Teaching Math 250: Linear algebra; and Math 348: Cryptography
Vita
Papers
Links

Department of Mathematics
Hill Center-Busch Campus
Rutgers, The State University of New Jersey
110 Frelinghuysen Rd
Piscataway, NJ 08854-8019

E-mail: miller@math.rutgers.edu
Office: Room 514 Hill Center
Phone: (848)-445-7967
Fax: (732)-445-5530

Some recent items: What's this background image?

Entirety of cuspidal Eisenstein series on loop groups, with Howard Garland and Manish Patnaik.

What mathematics is really behind the distributional Γ-factors? (for the Schmid 70th conference).

A p-adic integral for the reciprocal of L-functions, with Stephen Gelbart, Alexei Pantchichkine, and Freydoon Shahidi, to appear in a Contemporary Mathematics volume in memory of Ilya Piatetski-Shapiro.

Residual automorphic forms and spherical unitary representations of exceptional groups , to appear in Annals of Mathematics. Click here for the programs and data files.

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.

Fourier coefficients of automorphic forms, character variety orbits, and small representations, with Siddhartha Sahi, to appear in Journal of Number Theory.

The archimedean theory of the Exterior Square L-functions over Q, with Wilfried Schmid, to appear in Journal of the American Mathematical Society.,

Adelization of automorphic distributions and mirabolic Eisenstein series, with Wilfried Schmid, to appear in Contemporary Mathematics, volume in honor of Gregg Zuckerman's 60th birthday.

Pairings of automorphic distributions, with Wilfried Schmid, to appear in Mathematische Annalen.

On the rapid decay of cuspidal automorphic forms, with Wilfried Schmid, to appear in Advances in Mathematics.

Eisenstein series for higher-rank groups and string theory amplitudes, with Michael Green, Jorge Russo, and Pierre Vanhove, Communcations in Number Theory and Physics 4 (2010), 551-596.

Non-degeneracy of Pollard Rho Collisions, with Ramarathnam Venkatesan, International Mathematics Research Notices.

A method for computing general automorphic forms on general groups, Forum Mathematicum.

Conference on Analytic Number Theory and Higher Rank Groups, NYU, May 19-23, 2008. Power point for lectures 1 and 3, scanned notes for lecture 2.
(Click here for older powerpoint format.)

Non-abelian analogs of lattice rounding, with Evgeni Begelfor and Ramarathnam Venkatesan, preprint 2007.

MV3: A new word based stream cipher using rapid mixing and revolving buffers, with Nathan Keller, Ilya Mironov, and Ramarathnam Venkatesan, Topics in Cryptology -- CT-RSA 2007.

Spectral Analysis of Pollard Rho Collisions, with Ramarathnam Venkatesan, ANTS 2006.

The Rankin-Selberg method for automorphic distributions, with Wilfried Schmid, in .Representation Theory and Automorphic Forms, Birkhauser.

Slides from the Technion conference talk (12/20/2005) on "Applications of automorphic distributions to analytic number theory": powerpoint or html.

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.

Related Powerpoint presentations (can be viewed with a browser, e.g. Internet Explorer):

Chemistry and Graph Theory slides (10/14/2004)

Slides from a general talk (click here for the powerpoint file).