Zobrazeno 1 - 10
of 58
pro vyhledávání: '"Pete L Clark"'
Autor:
Pete L. Clark, Uwe Schauz
Publikováno v:
Journal of Algebra. 608:691-718
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::830c4e80afd4afb92379b5fe0fcbf48b
https://doi.org/10.1016/j.jalgebra.2022.05.035
https://doi.org/10.1016/j.jalgebra.2022.05.035
Publikováno v:
Journal of the London Mathematical Society. 105:825-883
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f6d8fd19b56b0a39488ffabf1a192ec9
https://doi.org/10.1112/jlms.12518
https://doi.org/10.1112/jlms.12518
Publikováno v:
Expositiones Mathematicae. 39:604-623
The Chevalley–Warning Theorem is a result on the solution set of a system of polynomial equations f 1 , … , f r in n variables over a finite field F q in the low degree case d ≔ ∑ j = 1 r deg ( f j ) n . In this note we reformulate that resul
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2994d244dee7498d4f2fc3510a88a3fd
https://doi.org/10.1016/j.exmath.2021.03.005
https://doi.org/10.1016/j.exmath.2021.03.005
Publikováno v:
The Ramanujan Journal. 55:1015-1037
Let F be a number field, and let $$F^{{\text {cyc}}}$$ be obtained by adjoining to F all the roots of unity. We show that as E ranges over all elliptic curves defined over $$F^{{\text {cyc}}}$$ with complex multiplication, the torsion subgroups $$E(F
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::37e777ed202a67cf938b4eab99af5a25
https://doi.org/10.1007/s11139-020-00271-0
https://doi.org/10.1007/s11139-020-00271-0
Autor:
Pete L. Clark, Paul Pollack
Publikováno v:
L’Enseignement Mathématique. 65:101-116
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::517e63a9771d866b935b78aa83f58f69
https://doi.org/10.4171/lem/65-1/2-3
https://doi.org/10.4171/lem/65-1/2-3
Publikováno v:
Proceedings of the American Mathematical Society. 147:4107-4122
We give conditions under which the number of solutions of a system of polynomial equations over a finite field F_q of characteristic p is divisible by p. Our setup involves the substitution t_i |-> f_i(t_i) for auxiliary polynomials f_1,...,f_n in F_
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4d6a2a41e52effeab6a1feba65b215ae
https://doi.org/10.1090/proc/14181
https://doi.org/10.1090/proc/14181
Autor:
Pete L. Clark
Publikováno v:
Mathematics Magazine. 92:136-150
We introduce real induction, a proof technique analogous to Mathematical Induction but applicable to statements indexed by an interval on the real line. We apply these principles to give streamline...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a36847fef968e7b9da8a93640de0c934
https://doi.org/10.1080/0025570x.2019.1549902
https://doi.org/10.1080/0025570x.2019.1549902
Autor:
Pete L. Clark
Publikováno v:
Journal of Algebraic Combinatorics. 48:325-349
We present a generalization of Warning’s second theorem to polynomial systems over a finite local principal ring with restricted input and relaxed output variables. This generalizes a recent result with Forrow and Schmitt (and gives a new proof of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::761500b899b7a6e986147d5a23336e4a
https://doi.org/10.1007/s10801-018-0836-0
https://doi.org/10.1007/s10801-018-0836-0
Publikováno v:
Combinatorics, Probability and Computing. 27:310-333
A 1993 result of Alon and F\"uredi gives a sharp upper bound on the number of zeros of a multivariate polynomial over an integral domain in a finite grid, in terms of the degree of the polynomial. This result was recently generalized to polynomials o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cf034882f164826502b852f6961c68f0
https://doi.org/10.1017/s0963548317000566
https://doi.org/10.1017/s0963548317000566
Autor:
Pete L. Clark
Publikováno v:
Expositiones Mathematicae. 35:350-356
We give an exposition of a recent result of M. Kapovich on the cardinal Krull dimension of the ring of holomorphic functions on a connected C -manifold. By reducing to the one-dimensional case we give a stronger lower bound for Stein manifolds.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7040963df4e83c75aabddfc271914f30
https://doi.org/10.1016/j.exmath.2017.03.001
https://doi.org/10.1016/j.exmath.2017.03.001