Number theory Sample Clauses
The 'Number theory' clause establishes the rules and principles governing the use, interpretation, or calculation of numbers within a given context, such as a contract or technical document. It may specify how numbers should be rounded, formatted, or interpreted (for example, whether decimals are permitted, or how fractions are handled), and can clarify whether numerical ranges are inclusive or exclusive. This clause ensures consistency and prevents misunderstandings related to numerical data, thereby reducing the risk of disputes over calculations or quantitative obligations.
Number theory. The prize rewards research results within these fields accessible to a large number of professional mathematicians. Therefore a brilliant result which could only be understood, interesting or useful to a limited number of specialized mathematicians cannot be considered. The jury will consider young mathematicians only (no older than 45 at the time of the submission of their application) and will prefer recent research results (obtained during the last five years). The Fermat Prize is not awarded to research groups, institutions or laboratories.
Number theory. The prime counting function
2.4.1. For a positive integer s and a prime p, write sp for the p-part of s. Also, define lpp s = maxp prime sp to be the largest prime power divisor of s. Fix s ≥ 2, and let k = lpp s. By writing the prime factorization of s as s = kpr2 . . . prt , one immediately sees that s ≤ kδ(k), where δ(k) denotes the number of primes less than or equal to k. Hence, log s ≤ δ(k) log k. Also, it is proved in [46, Corollary 1] that
Number theory. Academic Press, 1966. — 436 pp. [2] Cox ▇. ▇▇▇▇▇▇ of the form x2 + ny2: Fermat, Class Field Theory and Complex Multiplication. — ▇.▇▇▇▇▇ and Sons, 1989. — 363 pp.
Number theory. Algebraic and complex geometry
Number theory. Volume I: Tools and Diophantine equa- tions. Springer, 2007. [CP20] ▇▇▇▇▇▇▇▇▇ ▇▇▇▇▇▇▇▇ and ▇▇▇▇▇▇▇▇ ▇▇▇▇▇. Entanglement in the family of division fields of elliptic curves with complex multiplication. arXiv preprint arXiv:2006.00883, 2020. [CR21] ▇▇▇▇▇▇▇ ▇▇▇▇▇▇▇ and ▇▇▇▇▇▇ ▇▇▇▇▇. Uniform bounds on the image of the arboreal Galois representations attached to non-CM elliptic curves. Proceedings of the American Mathematical Society, 149(2):583–589, 2021. [Cre97] ▇▇▇▇ ▇. ▇▇▇▇▇▇▇. Algorithms for modular elliptic curves. Cambridge University Press, Cambridge, second edition, 1997. [CS19] ▇▇▇▇▇▇▇▇▇ ▇▇▇▇▇▇▇▇ and ▇▇▇▇▇ ▇▇▇▇▇▇▇▇▇▇▇. Cyclic reduction of ellip- tic curves. arXiv preprint arXiv:2001.00028, 2019. [Dav11] Agn`es ▇▇▇▇▇. Borne uniforme pour les homoth´eties dans l’image de ▇▇▇▇▇▇ associ´ee aux courbes elliptiques. Journal of Number Theory, 131(11):2175 – 2191, 2011. [Deu53] ▇▇▇ ▇▇▇▇▇▇▇. Die Zetafunktion einer algebraischen Kurve vom Geschlechte Eins. Nachrichten von der Akademie der Wissenschaften G¨ottingen Mathematisch-Physikalische Klasse. IIa, Mathematisch- Physikalisch-Chemische Abteilung, 1953:85–94, 1953. [Deu58] ▇▇▇ ▇▇▇▇▇▇▇. Die Klassenkorper der komplexen Multiplikation. In Enzyklop¨adie der mathematischen Wissenschaften, volume I2, Heft 10, Teil II. Teubner Verlag, Stuttgart, 1958. [DLM21] ▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇, A´▇▇▇▇▇ ▇▇▇▇▇▇-▇▇▇▇▇▇▇, and ▇▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇. Towards a classification of entanglements of Galois representations at- tached to elliptic curves. arXiv preprint arXiv:2105:02060, 2021. [DP16] ▇▇▇▇▇▇▇▇▇▇ ▇▇▇▇▇ and ▇▇▇▇▇▇▇▇▇ ▇▇▇▇▇▇▇. Reductions of algebraic in- tegers. Journal of Number Theory, 167:259–283, 2016. [EGH+11] ▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇, ▇▇▇▇ ▇▇▇▇▇▇▇, ▇▇▇▇▇▇▇▇▇ ▇▇▇▇▇▇, ▇▇▇▇▇▇▇ ▇▇▇, ▇▇▇▇ ▇▇▇▇▇▇▇▇▇▇, ▇▇▇▇▇▇ ▇▇▇▇▇▇▇▇, and ▇▇▇▇▇ ▇▇▇▇▇▇▇▇. Introduction to representation theory. American Mathematical Society, 2011. [ES53] ▇▇▇▇ ▇▇▇▇▇▇▇ and A ▇▇▇▇▇▇. U¨ ber injektive Moduln. Archiv der [Fle68] ▇▇▇▇▇▇▇ ▇▇▇▇▇▇▇▇▇. A new construction of the injective hull. Canadian Mathematical Bulletin, 11(1):19–21, 1968. [GM20] Aur´▇▇▇▇▇ ▇▇▇▇▇▇▇▇ and C´esar Mart´▇▇▇▇. Homoth´eties explicites des repr´esentations l-adiques. arXiv preprint arXiv:2006.07401, 2020. [Gou97] ▇▇▇▇▇▇▇▇ ▇. ▇▇▇▇ˆ▇▇. p-adic Numbers. Springer, 1997. [Gre12] ▇▇▇▇▇ ▇▇▇▇▇▇▇▇▇. The image of Galois representations attached to elliptic curves with an isogeny. American Journal of Mathematics, 134(5):1167–1196, 2012. [Gro91] ▇▇▇▇▇▇▇▇ ▇. ▇▇▇▇▇. ▇▇▇▇▇▇▇▇▇’s work on modular elliptic curves. In L- functions ...