Transcendental values of certain Eichler integrals,
... S2k (K) ∩ S2k (K) = {0}. This along with a result of Manin [24] implies that, for any normalized Hecke eigen cuspform f , L(j + 1, f )/π j+1 is either zero or transcendental for all 0 j 2k − 2. Applying Kohnen’s conjecture to the classical Eisenstein series, we have the transcendence of ζ(2k + 1 ...
... S2k (K) ∩ S2k (K) = {0}. This along with a result of Manin [24] implies that, for any normalized Hecke eigen cuspform f , L(j + 1, f )/π j+1 is either zero or transcendental for all 0 j 2k − 2. Applying Kohnen’s conjecture to the classical Eisenstein series, we have the transcendence of ζ(2k + 1 ...
2011 competition solutions - part i
... Method 1: From Vieta’s Theorem, we have q + r = –15 and qr = 31. Then, (q + 1) + (r + 1) = q + r + 2 = –13 and (q+1)(r+1) = qr + q + r + 1 = 31 – 15 + 1 = 17. Apply Vieta’s Theorem again to get the desired polynomial is x2 + 13x + 17. Method 2: One can imagine that increasing the roots both by 1 is ...
... Method 1: From Vieta’s Theorem, we have q + r = –15 and qr = 31. Then, (q + 1) + (r + 1) = q + r + 2 = –13 and (q+1)(r+1) = qr + q + r + 1 = 31 – 15 + 1 = 17. Apply Vieta’s Theorem again to get the desired polynomial is x2 + 13x + 17. Method 2: One can imagine that increasing the roots both by 1 is ...
I Can Statements
... I understand that a system of linear equations may have no solution, one solution, or an infinite number of solutions (and relate the number of solutions to pairs of lines that are intersecting, parallel or identical). ...
... I understand that a system of linear equations may have no solution, one solution, or an infinite number of solutions (and relate the number of solutions to pairs of lines that are intersecting, parallel or identical). ...
SummerLecture15.pdf
... In the example of the airplane, the function f gives the altitude of the plane at time t. Since the plane has an altitude at all times between 9:00 AM and 9:15 AM, the function is continuous on the interval [9:00 AM, 9:15 AM]. Using the designations from the formal statement of the theorem, a = 9 : ...
... In the example of the airplane, the function f gives the altitude of the plane at time t. Since the plane has an altitude at all times between 9:00 AM and 9:15 AM, the function is continuous on the interval [9:00 AM, 9:15 AM]. Using the designations from the formal statement of the theorem, a = 9 : ...
List of important publications in mathematics
This is a list of important publications in mathematics, organized by field.Some reasons why a particular publication might be regarded as important:Topic creator – A publication that created a new topicBreakthrough – A publication that changed scientific knowledge significantlyInfluence – A publication which has significantly influenced the world or has had a massive impact on the teaching of mathematics. Among published compilations of important publications in mathematics are Landmark writings in Western mathematics 1640–1940 by Ivor Grattan-Guinness and A Source Book in Mathematics by David Eugene Smith.