Galois representations of octahedral type and 2-coverings of elliptic curves.
Galois rings and algebraic cryptography
Galois structure of de Rham cohomology
Galois structure of ideals in wildly ramified abelian -extensions of a -adic field, and some applications
Let be a finite extension of with ramification index , and let be a finite abelian -extension with Galois group and ramification index . We give a criterion in terms of the ramification numbers for a fractional ideal of the valuation ring of not to be free over its associated order . In particular, if then the inverse different can be free over its associated order only when (mod ) for all . We give three consequences of this. Firstly, if is a Hopf order and is -Galois...
Galois theory and torsion points on curves
In this paper, we survey some Galois-theoretic techniques for studying torsion points on curves. In particular, we give new proofs of some results of A. Tamagawa and the present authors for studying torsion points on curves with “ordinary good” or “ordinary semistable” reduction at a given prime. We also give new proofs of : (1) the Manin-Mumford conjecture : there are only finitely many torsion points lying on a curve of genus at least embedded in its jacobian by an Albanese map; and (2) the...
Galois theory, elliptic curves, and root numbers
Galois towers over non-prime finite fields
We construct Galois towers with good asymptotic properties over any non-prime finite field ; that is, we construct sequences of function fields = (N₁ ⊂ N₂ ⊂ ⋯) over of increasing genus, such that all the extensions are Galois extensions and the number of rational places of these function fields grows linearly with the genus. The limits of the towers satisfy the same lower bounds as the best currently known lower bounds for the Ihara constant for non-prime finite fields. Towers with these properties...
Galois-Cohen-Lenstra heuristics
Galoismoduln mit Hasse-Prinzip.
Galoissche Kennzeichnung p-adisch abgeschlossener Körper.
Gamma-cohomology and the Selberg zeta function.
Ganzzahlige Funktionen natürlicher Zahlen.
Gaps between consecutive divisors of factorials
The set of all divisors of , ordered according to increasing magnitude, is considered, and an upper bound on the gaps between consecutive ones is obtained. We are especially interested in the divisors nearest and obtain a lower bound on their distance.
Gaps Between Consecutive Zeros of the Riemann Zeta-Function on the Critical Line.
Gaps between primes, and the pair correlation of zeros of the zeta-function
Gaps between primes in Beatty sequences
We study the gaps between primes in Beatty sequences following the methods in the recent breakthrough by Maynard (2015).
Gaps between values of positive definite quadratic forms
Gaps between zeros of the derivative of the Riemann -function
Assuming the Riemann hypothesis, we investigate the distribution of gaps between the zeros of . We prove that a positive proportion of gaps are less than times the average spacing and, in the other direction, a positive proportion of gaps are greater than times the average spacing. We also exhibit the existence of infinitely many normalized gaps smaller (larger) than (, respectively).
Gaps in dense Sidon sets.
Gaps in the sequence .