کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8896857 | 1630623 | 2018 | 39 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Hermite-Thue equation: Padé approximations and Siegel's lemma
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Hermite-Thue equation: Padé approximations and Siegel's lemma Hermite-Thue equation: Padé approximations and Siegel's lemma](/preview/png/8896857.png)
چکیده انگلیسی
Padé approximations and Siegel's lemma are widely used tools in Diophantine approximation theory. This work has evolved from the attempts to improve Baker-type linear independence measures, either by using the Bombieri-Vaaler version of Siegel's lemma to sharpen the estimates of Padé-type approximations, or by finding completely explicit expressions for the yet unknown 'twin type' Hermite-Padé approximations. The appropriate homogeneous matrix equation representing both methods has an MÃ(L+1) coefficient matrix, where Mâ¤L. The homogeneous solution vectors of this matrix equation give candidates for the Padé polynomials. Due to the Bombieri-Vaaler version of Siegel's lemma, the upper bound of the minimal non-zero solution of the matrix equation can be improved by finding the gcd of all the MÃM minors of the coefficient matrix. In this paper we consider the exponential function and prove that there indeed exists a big common factor of the MÃM minors, giving a possibility to apply the Bombieri-Vaaler version of Siegel's lemma. Further, in the case M=L, the existence of this common factor is a step towards understanding the nature of the 'twin type' Hermite-Padé approximations to the exponential function.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 191, October 2018, Pages 345-383
Journal: Journal of Number Theory - Volume 191, October 2018, Pages 345-383
نویسندگان
Tapani Matala-aho, Louna Seppälä,