Linear forms in p-adic logarithms
نویسندگان
چکیده
منابع مشابه
p-ADIC LOGARITHMS FOR POLYNOMIAL DYNAMICS
We prove a dynamical version of the Mordell-Lang conjecture for subvarieties of the affine space A over a p-adic field, endowed with polynomial actions on each coordinate of A. We use analytic methods similar to the ones employed by Skolem, Chabauty, and Coleman for studying diophantine equations.
متن کاملOn Wieferich primes and p-adic logarithms∗†
We shall make a slight improvement to a result of p-adic logarithms which gives a nontrivial upper bound for the exponent of p dividing the Fermat quotient x − 1.
متن کاملEstimates for linear forms in logarithms
The dependence on the Ai’s is very satisfactory, unlike the dependence on B. However, for applications to Diophantine problems, we need a better estimate in terms of B, even if it means to get a weaker one in terms of the Ai’s. Alan Baker [1, 2] was the first to prove such a result, and we are now able to show that, under the above assumptions, there exists an effectively computable constant c(...
متن کاملZeros of p-adic forms
A variant of Brauer’s induction method is developed. It is shown that quartic p-adic forms with at least 9127 variables have non-trivial zeros, for every p. For odd p considerably fewer variables are needed. There are also subsidiary new results concerning quintic forms, and systems of forms.
متن کاملp-adic aspects of Jacobi forms
We are interested in understanding and describing the p-adic properties of Jacobi forms. As opposed to the case of modular forms, not much work has been done in this area. The literature includes [3, 4, 7]. In the first section, we follow Serre’s ideas from his theory of p-adic modular forms. We study Jacobi forms whose Fourier expansions have integral coefficients and look at congruences betwe...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1989
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-53-2-107-186