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Dinesh Thakur (mathematician)
(400 words)
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Rochester in July 2013. Thakur wrote a research monograph Function Field Arithmetic. Thakur has been serving on the editorial boards of Journal of NumberThin set (Serre) (1,021 words) [view diff] case mismatch in snippet view article
A discussion on these results and more appears in Fried-Jarden's Field Arithmetic. Being Hilbertian is at the other end of the scale from being algebraicallyCarlitz exponential (377 words) [view diff] exact match in snippet view article find links to article
the Carlitz module. Goss, D. (1996). Basic structures of function field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in MathematicsGoss zeta function (151 words) [view diff] exact match in snippet view article find links to article
Goss zeta function. Goss, David (1996), Basic structures of function field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in MathematicsAlgebraic closure (992 words) [view diff] exact match in snippet view article find links to article
12009. McCarthy (1991) p.22 Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11Faltings's theorem (1,318 words) [view diff] case mismatch in snippet view article find links to article
Faltings's theorem Gerd Faltings Field Arithmetic geometry Conjectured by Louis Mordell Conjectured in 1922 First proof by Gerd Faltings First proof inMoore matrix (496 words) [view diff] case mismatch in snippet view article find links to article
Goss (1996). "1. Additive Polynomials". Basic Structures of Function Field Arithmetic. Springer. pp. 1–33. doi:10.1007/978-3-642-61480-4_1. ISBN 3-540-63541-6Absolute Galois group (950 words) [view diff] exact match in snippet view article find links to article
258: 5305–5308, MR 0162796 Fried, Michael D.; Jarden, Moshe (2008), Field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 11Primary extension (145 words) [view diff] exact match in snippet view article find links to article
Fried & Jarden (2008) p.44 Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11Michel Raynaud (654 words) [view diff] exact match in snippet view article find links to article
S2CID 121690794. Zbl 0805.14014.. Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11Embedding problem (413 words) [view diff] case mismatch in snippet view article find links to article
1090/mmono/165. ISBN 9780821845929. Fried, Michael D.; Jarden, Moshe (2008). Field Arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A SeriesAbhyankar's conjecture (459 words) [view diff] exact match in snippet view article find links to article
1007/BF01232232, Zbl 0805.14014. Fried, Michael D.; Jarden, Moshe (2008), Field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 11Pseudo algebraically closed field (542 words) [view diff] exact match in snippet view article find links to article
Fried & Jarden (2008) p.462 Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11Pseudo-finite field (156 words) [view diff] exact match in snippet view article find links to article
MR 0229613, Zbl 0195.05701 Fried, Michael D.; Jarden, Moshe (2008), Field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 11Regular extension (341 words) [view diff] exact match in snippet view article find links to article
(2008) p.44 Cohn (2003) p.427 Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11Formation (group theory) (419 words) [view diff] exact match in snippet view article
ISBN 978-3-11-012892-5, MR 1169099 Fried, Michael D.; Jarden, Moshe (2004), Field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 11Quantifier elimination (1,435 words) [view diff] exact match in snippet view article find links to article
ISBN 978-0-12-238452-3. Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11Hilbert's irreducibility theorem (732 words) [view diff] case mismatch in snippet view article find links to article
The Mordell-Weil Theorem, Vieweg, 1989. M. D. Fried and M. Jarden, Field Arithmetic, Springer-Verlag, Berlin, 2005. H. Völklein, Groups as Galois GroupsAdditive polynomial (644 words) [view diff] case mismatch in snippet view article find links to article
Drinfeld module Additive map David Goss, Basic Structures of Function Field Arithmetic, 1996, Springer, Berlin. ISBN 3-540-61087-1. Weisstein, Eric W. "AdditiveHaran's diamond theorem (339 words) [view diff] case mismatch in snippet view article find links to article
S2CID 120002473, Zbl 0933.12003. Fried, Michael D.; Jarden, Moshe (2008), Field Arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3 Folge, vol. 11Supernatural number (595 words) [view diff] exact match in snippet view article find links to article
ISBN 0-8218-4041-X. Zbl 1103.12002. Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11David Goss (339 words) [view diff] exact match in snippet view article find links to article
Mathematical Society. Goss, David (1996), Basic structures of function field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in MathematicsCover (algebra) (378 words) [view diff] exact match in snippet view article
Lawson p. 230 Grilett p. 360 Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11Zeev Rudnick (682 words) [view diff] exact match in snippet view article find links to article
Jean Bourgain). Another interest is the interface between function field arithmetic and corresponding problems in number fields. Ph.D., 1990, Yale UniversityGlossary of field theory (2,063 words) [view diff] exact match in snippet view article find links to article
ISBN 1-85233-587-4. Zbl 1003.00001. Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11Newton polygon (2,413 words) [view diff] exact match in snippet view article find links to article
Curves, pp. 370–383. Goss, David (1996), Basic structures of function field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in MathematicsElliptic-curve cryptography (4,676 words) [view diff] exact match in snippet view article find links to article
Diffie–Hellman key exchanges. This key exchange uses much of the same field arithmetic as existing elliptic curve cryptography and requires computationalQuasi-algebraically closed field (1,067 words) [view diff] exact match in snippet view article find links to article
JSTOR 2373065. Zbl 0136.32805. Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11Sato–Tate conjecture (1,420 words) [view diff] case mismatch in snippet view article find links to article
Sato–Tate conjecture Field Arithmetic geometry Conjectured by Mikio Sato John Tate Conjectured in c. 1960 First proof by Laurent Clozel Thomas Barnet-LambCipolla's algorithm (3,042 words) [view diff] exact match in snippet view article find links to article
\omega } can roughly be seen as analogous to the complex number i. The field arithmetic is quite obvious. Addition is defined as ( x 1 + y 1 ω ) + ( x 2 +Profinite group (2,609 words) [view diff] exact match in snippet view article find links to article
procyclic groups". MathOverflow. Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11Crypto++ (1,341 words) [view diff] exact match in snippet view article find links to article
multi-precision integers; prime number generation and verification; finite field arithmetic, including GF(p) and GF(2n); elliptical curves; and polynomial operationsNielsen–Schreier theorem (1,691 words) [view diff] exact match in snippet view article find links to article
Mathematica, 3: 391–398. Fried, Michael D.; Jarden, Moshe (2008), Field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 11Function field sieve (2,658 words) [view diff] case mismatch in snippet view article find links to article
Inform. Theory IT-39 (1984), pp. 587-594. M. Fried and M. Jarden. In: "Field Arithmetic". vol. 11. (Jan. 2005). Chap. 2.1. DOI: 10.1007/b138352. D. GordonDrinfeld module (1,623 words) [view diff] exact match in snippet view article find links to article
23 (1974) 561–592. Goss, David (1996), Basic structures of function field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in MathematicsNumber theory (11,121 words) [view diff] case mismatch in snippet view article find links to article
Fermat Prize. Mathematics portal Arithmetic dynamics Algebraic function field Arithmetic topology Finite field p-adic number List of number theoretic algorithmsTwisted polynomial ring (617 words) [view diff] exact match in snippet view article find links to article
division algorithms. Goss, D. (1996), Basic structures of function field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in MathematicsVector processor (8,675 words) [view diff] exact match in snippet view article find links to article
linear vector data. Advanced Math formats – often includes Galois field arithmetic, but can include binary-coded decimal or decimal fixed-point, and supportSeparable extension (3,075 words) [view diff] exact match in snippet view article find links to article
Cohn (2003). Basic algebra Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11Field of definition (1,617 words) [view diff] case mismatch in snippet view article find links to article
isomorphically onto a σ(L)-variety. Fried, Michael D.; Moshe Jarden (2005). Field Arithmetic. Springer. p. 780. doi:10.1007/b138352. ISBN 3-540-22811-X. The terminologyBarrett reduction (3,763 words) [view diff] exact match in snippet view article find links to article
at the end of an algorithm at the expense of larger inputs to the field arithmetic operations. The Barrett multiplication previously described requires