Finite cotangent sums and the Riemann zeta function
Finite Groups and Hecke Operators.
Finite Knot Modules and the Factorization of Certain Simple Knots.
Finite Polynomial Orbits in Finitely Generated Domains.
Finite projective planes, Fermat curves, and Gaussian periods
One of the oldest and most fundamental problems in the theory of finite projective planes is to classify those having a group which acts transitively on the incident point-line pairs (flags). The conjecture is that the only ones are the Desarguesian projective planes (over a finite field). In this paper, we show that non-Desarguesian finite flag-transitive projective planes exist if and only if certain Fermat surfaces have no nontrivial rational points, and formulate several other equivalences involving...
Finite Rogers-Ramanujan type identities.
Finite spanning sets for cusp forms and a related geometric result.
Finite subgroups of .
Finite vector spaces and certain lattices.
Finiteness criteria for decomposable form equations
Finiteness of a class of Rabinowitsch polynomials
We prove that there are only finitely many positive integers such that there is some integer such that is 1 or a prime for all , thus solving a problem of Byeon and Stark.
Finiteness of odd perfect powers with four nonzero binary digits
We prove that there are only finitely many odd perfect powers in having precisely four nonzero digits in their binary expansion. The proofs in fact lead to more general results, but we have preferred to limit ourselves to the present statement for the sake of simplicity and clarity of illustration of the methods. These methods combine various ingredients: results (derived from the Subspace Theorem) on integer values of analytic series at -unit points (in a suitable -adic convergence), Roth’s...
Finiteness properties of soluble arithmetic groups over global function fields.
Finiteness results for Diophantine triples with repdigit values
Let g ≥ 2 be an integer and be the set of repdigits in base g. Let be the set of Diophantine triples with values in ; that is, is the set of all triples (a,b,c) ∈ ℕ³ with c < b < a such that ab + 1, ac + 1 and bc + 1 lie in the set . We prove effective finiteness results for the set .
Finiteness Theorems for Deformations of Complexes
We consider deformations of bounded complexes of modules for a profinite group over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex to be represented by a complex of -modules that is strictly perfect over the associated versal deformation ring.
Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups
Finiteness theorems for factorizations.
Finiteness theorems for forms over global fields.
Finiteness theorems for torsion of abelian varieties over large algebraic fields
Finitude de tours et -tours -ramifiées modérées, -décomposées
Soit un corps de nombres et soient et deux ensembles finis de places de ; on peut définir la tour de Hilbert de , -ramifiée modérée, -décomposée. Ceci permet d’obtenir, par exemple, la notion de tour de Hilbert au sens classique et de tour de Hilbert au sens restreint. On donne alors d’une part, un critère de finitude de cette nouvelle tour, critère construit à partir d’un résultat d’Odlyzko, puis d’autre part deux critères de non-finitude, le premier étant une conséquence d’un résultat...