منابع مشابه
Davenport-Hasse theorem and cyclotomic association schemes
Definition. Let q be a prime power and e be a divisor of q − 1. Fix a generator α of the multiplicative group of GF (q). Then 〈α〉 is a subgroup of index e and its cosets are 〈α〉α, i = 0, . . . , e− 1. Define R0 = {(x, x)|x ∈ GF (q)} Ri = {(x, y)|x, y ∈ GF (q), x− y ∈ 〈αe〉αi−1}, (1 ≤ i ≤ e) R = {Ri|0 ≤ i ≤ e} Then (GF (q),R) forms an association scheme and is called the cyclotomic scheme of clas...
متن کاملOn the Hasse Principle for Shimura Curves
Let C be an algebraic curve defined over a number field K, of positive genus and without K-rational points. We conjecture that there exists some extension field L over which C violates the Hasse principle, i.e., has points everywhere locally but not globally. We show that our conjecture holds for all but finitely many Shimura curves of the form XD 0 (N)/Q or X D 1 (N)/Q, where D > 1 and N are c...
متن کاملHasse Invariants for the Clausen Elliptic Curves
Gauss’s 2F1 ( 1 2 1 2 1 | x ) hypergeometric function gives periods of elliptic curves in Legendre normal form. Certain truncations of this hypergeometric function give the Hasse invariants for these curves. Here we study another form, which we call the Clausen form, and we prove that certain truncations of 3F2 ( 1 2 1 2 1 2 1 1 | x ) and 2F1 ( 1 4 3 4 1 | x ) in Fp[x] are related to the charac...
متن کاملThe Hasse Principle and the Brauer-manin Obstruction for Curves
We discuss a range of ways, extending existing methods, to demonstrate violations of the Hasse principle on curves. Of particular interest are curves which contain a rational divisor class of degree 1, even though they contain no rational point. For such curves we construct new types of examples of violations of the Hasse principle which are due to the Brauer-Manin obstruction, subject to the c...
متن کاملCurves over Global Fields Violating the Hasse Principle
We exhibit for each global field k an algebraic curve over k which violates the Hasse Principle. We can find such examples among Atkin-Lehner twists of certain elliptic modular curves and Drinfeld modular curves. Our main tool is a refinement of the “Twist Anti-Hasse Principle” (TAHP). We then use TAHP to construct further Hasse Principle violations, e.g. among curves over any number field of a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1968
ISSN: 0025-5645
DOI: 10.2969/jmsj/02010403