Norm form equations with solutions taking values in a multi-recurrence
نویسندگان
چکیده
We are interested in solutions of a norm form equation that takes values given multi-recurrence. show among the there only finitely many each component which lie multi-recurrence unless recurrence is precisely described exceptional shape. This gives variant question on arithmetic progressions solution set equations.
منابع مشابه
On the number of solutions of norm form equations
A norm form is a form F(X" ... ,Xn ) with rational coefficients which factors into linear forms over C but is irreducible or a power of an irreducible form over Q. It is known that a nondegenerate norm form equation F(x" .... xn) = m has only finitely many. solutions (XI, .... Xn) E zn. We derive explicit bounds for the number of solutions. When F has coefficients in Z. these bounds depend only...
متن کاملParameterized norm form equations with arithmetic progressions
Buchmann and Pethő [5] observed that following algebraic integer 10 + 9α + 8α + 7α + 6α + 5α + 4α, with α = 3 is a unit. Since the coefficients form an arithmetic progressions they have found a solution to the Diophantine equation (1) NK/Q(x0 + αx1 + · · ·+ x6α) = ±1, such that (x0, . . . , x6) ∈ Z is an arithmetic progression. Recently Bérczes and Pethő [3] considered the Diophantine equation ...
متن کاملComputing small solutions of unit equations in three variables I: Application to norm form equations
We construct an algorithm to enumerate small solutions of unit equations in three variables. The algorithm is a generalization of K.Wildanger’s method [17] and of the method of I.Gaál and M.Pohst [6], and is based on the method of U.Fincke and M.Pohst [4] enumerating lattice points in ellipsoids (see also I.Gaál [5]). We will call a solution small if it has ”small” exponents corresponding to a ...
متن کاملNorm Form Equations and Continued Fractions
We consider the Diophantine equation of the form x2−Dy2 = c, where c ∣∣ 2D, gcd(x, y) = 1, and provide criteria for solutions in terms of congruence conditions on the fundamental solution of the Pell Equation x2 − Dy2 = 1. The proofs are elementary, using only basic properties of simple continued fractions. The results generalize various criteria for such solutions, and expose the central norm,...
متن کاملExtremal solutions for stochastic equations indexed by negative integers and taking values in compact groups
Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied to characterize several properties of the set of all solutions in terms of the law of the driving noise.
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: Acta Arithmetica
سال: 2021
ISSN: ['0065-1036', '1730-6264']
DOI: https://doi.org/10.4064/aa200622-22-10