His interests include asymptotically fast arithmetic—he wrote a book on algorithms for computer arithmetic with Richard Brent. He has developed some of the fastest available code for manipulating polynomials over GF(2), and for calculating hypergeometric constants to billions of decimal places. He is associated with the CARAMEL project to develop efficient arithmetic, in a general context and in particular in the context of algebraic curves of small genus; arithmetic on polynomials of very large degree turns out to be useful in algorithms for point-counting on such curves. He is also interested in computational number theory. In particular, he has contributed to some of the record computations in integer factorisation  and discrete logarithm.
Zimmermann's Erdős number is 2.
In a 2014 blog post, Zimmerman said that he would refuse invitations to review papers submitted to gold (author-pays) open access and hybrid open access journals, because he disagrees with the publication mechanism.
- P. Zimmermann; R.Brent. "Modern Computer Arithmetic".
- Paul Zimmermann; Richard P. Brent; Pierrick Gaudry; Emmanuel Thomé (2008). Poorten, Alfred J.; Stein, Andreas, eds. "Faster Multiplication in GF(2)[x]". Proceedings of ANTS-VIII. Lecture Notes in Computer Science 5011: 153–166. doi:10.1007/978-3-540-79456-1. ISBN 978-3-540-79455-4.
- Paul Zimmermann; Howard Cheng; Guillaume Hanrot; Emmanuel Thomé; Eugene Zima (2007). C W Brown, ed. Time- and Space-Efficient Evaluation of Some Hypergeometric Constants. Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC) 2007. pp. 85–91.
- Cryptology ePrint Archive: Report 2010/006
- Cryptology ePrint Archive: Report 2013/197
- P. Zimmermann. "Why I refuse to review papers submitted to open-access and hybrid journals?".
- Flajolet, Philippe; Zimmerman, Paul; Van Cutsem, Bernard (1994). "A calculus for the random generation of labelled combinatorial structures". Theoretical Computer Science 132 (1): 1–35. doi:10.1016/0304-3975(94)90226-7. MR 1290534.
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