An extension of the Siegel-Walfisz theorem

AN ANALOGUE OF THE SIEGEL-WALFISZ THEOREM FOR THE CYCLICITY OF CM ELLIPTIC CURVES MOD p

Let E be a CM elliptic curve defined over Q and of conductor N . We establish an asymptotic formula, uniform in N and with improved error term, for the counting function of primes p for which the reduction mod p of E is cyclic. Our result resembles the classical Siegel-Walfisz theorem regarding the distribution of primes in arithmetic progressions.

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

Improvement of a Theorem of Linnik and Walfisz 423 Improvement of a Theorem of Linnik and Walfisz

The Siegel-shidlovskii Theorem Revisited

Using Y.André's result on differential equations staisfied by E-functions, we derive an improved version of the Siegel-Shidlovskii theorem. It gives a complete characterisation of algebraic relations over the algebraic numbers between values of E-functions at any non-zero algebraic point.

The Thue–Siegel–Roth Theorem

In this paper we will give a proof of the Thue-Siegel-Roth Theorem, which states that for any algebraic number α and any ǫ > 0 there exists only a finite number of pairs of coprime integers p, q such that ∣ α − p q ∣ ∣ < 1 q2+ǫ . We will follow the proof as it is presented Leveque’s book, [8, ch 4]. This proof also deals with the more general case when p q is allowed to be an algebraic number i...