University of California - Berkeley University of Michigan
Scientific career
Fields
Computer Science
Institutions
University of Wisconsin - Madison
Doctoral advisor
Manuel Blum
Doctoral students
John Watrous Victor Shoup
Eric Bach is an American computer scientist who has made contributions to computational number theory.
Bach completed his undergraduate studies at the University of Michigan, Ann Arbor, and got his Ph.D. in computer science from the University of California, Berkeley, in 1984 under the supervision of Manuel Blum.[1] He is currently a professor at the Computer Science Department, University of Wisconsin–Madison.
Among other work, he gave explicit bounds for the Chebotarev density theorem, which imply that if one assumes the generalized Riemann hypothesis then is generated by its elements smaller than 2(log n)2.[2] This result shows that the generalized Riemann hypothesis implies tight bounds for the necessary run-time of the deterministic version of the Miller–Rabin primality test. Bach also did some of the first work on pinning down the actual expected run-time of the Pollard rho method where previous work relied on heuristic estimates and empirical data.[3] He is the namesake of Bach's algorithm for generating random factored numbers.
^"Eric Bach". ACM SIGACT Theoretical Computer Science genealogy database. Archived from the original on November 27, 2005. Retrieved 2008-06-04.
^Bach, Eric (1990), "Explicit bounds for primality testing and related problems", Mathematics of Computation, 55 (191): 355–380, doi:10.2307/2008811, JSTOR 2008811
^Bach, Eric (1991). "Toward a theory of Pollard's rho method" (PDF). Information and Computation. 90 (2): 139–155. doi:10.1016/0890-5401(91)90001-i. Retrieved March 4, 2015.
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SageMath Number Theory Library PARI/GP Fast Library for Number Theory EricBach; Jeffrey Shallit (1996). Algorithmic Number Theory, Volume 1: Efficient...
advisor Marvin Minsky Doctoral students Leonard Adleman Dana Angluin C. EricBach Shafi Goldwasser Mor Harchol-Balter Russell Impagliazzo Silvio Micali...
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University IBM Zurich Research Lab Thesis "Removing Randomness from Computational Number Theory" (1989) Doctoral advisor EricBach Website www.shoup.net...
their computational models to all be equivalent to the complex numbers. (EricBach points out that this equivalence can be seen as a form of the Lefschetz...
fined 60 million HUF (approximately US$280,000). In 2007, author Richard Bach made claims against the company for copyright infringement and trademark...
Concertos (BWV 1046–1051) by Johann Sebastian Bach are a collection of six instrumental works presented by Bach to Christian Ludwig, Margrave of Brandenburg-Schwedt...
"Five Things to Know About New Chiefs' OC Eric Bieniemy". chiefs.com. Retrieved February 27, 2023. Bach, Jessica; Tran, Bruce (April 5, 2004). "Football:...
(2008). His publications include the books Algorithmic Number Theory (with EricBach), a noted text on algorithms, Automatic Sequences: Theory, Applications...
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