zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Prime numbers and computer methods for factorization. 2nd ed. (English) Zbl 0821.11001
Progress in Mathematics (Boston, Mass.). 126. Boston, MA: Birkhäuser. xvi, 464 p. DM 158.00; öS 1232.40; sFr. 138.00; £ 69.00; FF 610.00 (1994).
Here is an outstanding technical monograph on recursive number theory and its numerous automated techniques. It successfully passes a critical milestone not allowed to many books, viz., a second edition. For a review of the first edition (1985) written by {\it H. J. te Riele} see Zbl 0582.10001. Many good things have happened to computational number theory during the ten years since the first edition appeared and the author includes their highlights in great depth. Several major sections have been rewritten and totally new sections have been added. The new material includes advances on applications of the elliptic curve method, uses of the number field sieve, and two new appendices on the basics of higher algebraic number fields and elliptic curves. Further, the table of prime factors of Fermat numbers has been significantly up-dated; e.g., now it is known that $F\sb 9$ is tri-composite and $F\sb{11}$ is penta-composite. Several other tables have been added so as to provide data to look for large prime factors of certain “generalized” Fermat numbers, while several other tables on special numbers were simply deleted in the second edition. Still one can make several perplexing assertions or challenges: (1) prove that $F\sb 5$, $F\sb 6$, $F\sb 7$, $F\sb 8$ are the only four consecutive Fermat numbers which are bi-composite; (2) Show that $F\sb{14}$ is bi- composite. (This accounts for the difficulty in finding a prime factor for it.) (3) What is the smallest Fermat quadri-composite?; and (4) Does there exist a Fermat number with an arbitrarily prescribed number of prime factors? All in all, this handy volume continues to be an attractive combination of number-theoretic precision, practicality, and theory with a rich blend of computer science.

11-01Textbooks (number theory)
11-02Research monographs (number theory)
11YxxComputational number theory
11-04Machine computation, programs (number theory)
11Y16Algorithms; complexity (number theory)
11N05Distribution of primes
11A41Elementary prime number theory
11A51Factorization; primality
68Q25Analysis of algorithms and problem complexity