ISSN 1088-6850(online) ISSN 0002-9947(print)

Effective -adic bounds for solutions of homogeneous linear differential equations

Authors: B. Dwork and P. Robba
Journal: Trans. Amer. Math. Soc. 259 (1980), 559-577
MSC: Primary 12B40; Secondary 14G20
DOI: https://doi.org/10.1090/S0002-9947-1980-0567097-1
MathSciNet review: 567097
Full-text PDF Free Access

Abstract: We consider a finite set of power series in one variable with coefficients in a field of characteristic zero having a chosen nonarchimedean valuation. We study the growth of these series near the boundary of their common ``open'' disk of convergence. Our results are definitive when the wronskian is bounded. The main application involves local solutions of ordinary linear differential equations with analytic coefficients. The effective determination of the common radius of convergence remains open (and is not treated here).

[Enhancements On Off] (What's this?)

•  P. Deligne, Équations différentielles à points singuliers réguliers, Lecture Notes in Math., vol. 163, Springer, Berlin and New York, 1970.
•  Bernard Dwork, On the zeta function of a hypersurface. II, Ann. of Math. (2) 80 (1964), 227–299. MR 188215, https://doi.org/10.2307/1970392
•  -, p-adic cycles, Publ. Math. Inst. Hautes Études Sci., No. 37, 1969.
•  B. M. Dwork, On 𝑝-adic differential equations. I. The Frobenius structure of differential equations, Table Ronde d’Analyse non archimédienne (Paris, 1972) Soc. Math. France, Paris, 1974, pp. 27–37. Bull. Soc. Math. France, Mém. No. 39-40. MR 0571892, https://doi.org/10.24033/msmf.161
•  Bernard Dwork, On ordinary linear 𝑝-adic differential equations with algebraic function coefficients, Groupe d’Étude d’Analyse Ultramétrique, 3e année (1975/76), Fasc. 1, Exp. No. 18, Secrétariat Math., Paris, 1977, pp. 10. MR 0506274
•  B. Dwork and P. Robba, On ordinary linear 𝑝-adic differential equations, Trans. Amer. Math. Soc. 231 (1977), no. 1, 1–46. MR 447247, https://doi.org/10.1090/S0002-9947-1977-0447247-8
•  G. Frobenius, Ueber der Begriff der Irreductibilitä, in Theorie der linear Differentialgleichungen, J. Reine Angew. Math. 76 (1873), 236-270.
• [7a] -, Über die Determinante mehrerer Functionen einer Variabeln, J. Reine Angew. Math. 77 (1874), 245-257.
•  Nicholas Katz, Travaux de Dwork, Séminaire Bourbaki, 24ème année (1971/1972), Exp. No. 409, Springer, Berlin, 1973, pp. 167–200. Lecture Notes in Math., Vol. 317 (French, with English summary). MR 0498577
•  E. Poole, Introduction to the theory of linear differential equations, Oxford Univ. Press, Oxford, 1936.
•  P. Robba, On the index of 𝑝-adic differential operators. I, Ann. of Math. (2) 101 (1975), 280–316. MR 364243, https://doi.org/10.2307/1970992
•  -, Nouveaupoint de vue sur le prolongement algébrique, Groupe d'Étude d'Analyse Ultramétrique 1976/77, exposé 5, Secrétariat Math., Paris.
•  -, Disque générique et équations différentielles, Groupe d'Étude d'Analyse Ultramétrique 1976/77, exposé 8, Secrétariat Math., Paris.
•  P. Robba and B. Dwork, Sur les équations différentielles linéaires p-adiques. II, Trans. Amer. Math. Soc. (to appear).

Retrieve articles in Transactions of the American Mathematical Society with MSC: 12B40, 14G20

Retrieve articles in all journals with MSC: 12B40, 14G20
{"ft_lang_label":"__label__en","ft_lang_prob":0.52935946,"math_prob":0.7112853,"size":3440,"snap":"2020-24-2020-29","text_gpt3_token_len":1107,"char_repetition_ratio":0.110593714,"word_repetition_ratio":0.012448133,"special_character_ratio":0.3473837,"punctuation_ratio":0.2689655,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.971229,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-15T06:07:52Z\",\"WARC-Record-ID\":\"<urn:uuid:27e8d067-3d04-4108-a1b1-a6cfd075838e>\",\"Content-Length\":\"46626\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c0c17cc6-a0c2-4690-a759-4745c3f19461>\",\"WARC-Concurrent-To\":\"<urn:uuid:7dee4dcd-4587-49e4-99e7-2ac73a9795b9>\",\"WARC-IP-Address\":\"130.44.204.100\",\"WARC-Target-URI\":\"https://www.ams.org/journals/tran/1980-259-02/S0002-9947-1980-0567097-1/home.html\",\"WARC-Payload-Digest\":\"sha1:XMEYBK6H4ZFB2IDQQ7FYLUUABX7UNCV4\",\"WARC-Block-Digest\":\"sha1:6MK3HZMJR5AJSSISOPVRVMBZYIYFYGGS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593657155816.86_warc_CC-MAIN-20200715035109-20200715065109-00017.warc.gz\"}"}