series with non-zero central critical value
... that of Bump, Friedberg and Hoffstein [3] (see also [10] for a shorter proof), that if E is a modular elliptic curve and, if L(E, 1) 6= 0, then the rank of E is 0. Thus, if f has the property that a positive proportion of the twists of L(f, s) have nonzero central critical value, then this implies t ...
... that of Bump, Friedberg and Hoffstein [3] (see also [10] for a shorter proof), that if E is a modular elliptic curve and, if L(E, 1) 6= 0, then the rank of E is 0. Thus, if f has the property that a positive proportion of the twists of L(f, s) have nonzero central critical value, then this implies t ...
e-print - Lebanon Valley College
... Before the discovery of irrationals, it was assumed that any two segments could be measured by whole number multiples of some common measuring stick. The existence of irrational numbers implies that this is not always possible. Here is the formal vocabulary used to discuss these ideas. Lengths A and ...
... Before the discovery of irrationals, it was assumed that any two segments could be measured by whole number multiples of some common measuring stick. The existence of irrational numbers implies that this is not always possible. Here is the formal vocabulary used to discuss these ideas. Lengths A and ...
MA3A9. Students will use sequences and series
... The launching activity begins by revisiting ideas of arithmetic sequences studied in eighth and ninth grades. Definitions, as well as the explicit and recursive forms of arithmetic sequences are reviewed. The task then introduces summations, including notation and operations with summations, and sum ...
... The launching activity begins by revisiting ideas of arithmetic sequences studied in eighth and ninth grades. Definitions, as well as the explicit and recursive forms of arithmetic sequences are reviewed. The task then introduces summations, including notation and operations with summations, and sum ...
Unit 2 Sequences and Series
... summation, and 1 is the lower limit of summation. This expression gives the partial sum, the sum n ...
... summation, and 1 is the lower limit of summation. This expression gives the partial sum, the sum n ...
Infinity
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.In mathematics, ""infinity"" is often treated as if it were a number (i.e., it counts or measures things: ""an infinite number of terms"") but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number; see 1/∞.Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.