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{{Infobox scientist | |||
| name = Eric Bach | |||
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| field = [[Computer Science]] | |||
| work_institution = [[University of Wisconsin - Madison]] | |||
| alma_mater = [[University of California - Berkeley]]<br>[[University of Michigan - Ann Arbor]] | |||
| doctoral_advisor = [[Manuel Blum]] | |||
| doctoral_students = [[John Watrous (computer scientist)|John Watrous]]<br>[[Victor Shoup]] | |||
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| religion =germaen | |||
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'''Eric Bach''' is an [[United States|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]].<ref>{{cite web | title = Eric Bach | url = http://sigact.acm.org/cgi-bin/genealogy.cgi?file=database-B.html&from=Bach,Eric&to=endhere | work = [[ACM SIGACT]] Theoretical Computer Science genealogy database | accessdate = 2008-06-04}} {{Dead link|date=October 2010|bot=H3llBot}}</ref> 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 <math>\left(\mathbb{Z}/n\mathbb{Z}\right)^*</math> is generated by its elements smaller than 2(log ''n'')<sup>2</sup>.<ref>{{Citation |last=Bach |first=Eric |year=1990 |title=Explicit bounds for primality testing and related problems |journal=Mathematics of Computation |volume=55 |issue=191 |pages=355–380 |doi=10.2307/2008811 |issn= }}</ref> 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's rho algorithm|Pollard rho method]] where previous work relied on heuristic estimates and empirical data.<ref>{{cite journal|last=Bach|first=Eric|title=Toward a theory of Pollard's rho method.|journal=Information and Computation|year=1991|volume=90|issue=2|pages=139–155|accessdate=March 1, 2011}}</ref> | |||
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{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. --> | |||
| NAME = Bach, Eric | |||
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| SHORT DESCRIPTION = American computer scientist | |||
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[[Category:American computer scientists]] | |||
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[[Category:University of Michigan alumni]] | |||
[[Category:University of California, Berkeley alumni]] | |||
[[Category:University of Wisconsin–Madison faculty]] | |||
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Revision as of 00:36, 15 September 2013
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]
References
- ↑ Template:Cite web Template:Dead link
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