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<p class="MsoTitle"><span
style="font-size:18.0pt;font-family:"Times New
Roman","serif"">SEMINARIO
<span style="mso-no-proof:yes">MATEMATICA</span><o:p></o:p></span></p>
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style="font-size:10.0pt;font-family:"Times New
Roman","serif""><o:p><span
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<p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
line-height:18.0pt;tab-stops:324.0pt" align="center"><span
style="font-size:16.0pt;font-family:
"Times New Roman","serif";mso-no-proof:yes">Giovedì
20 giugno 2013</span><span
style="font-size:16.0pt;font-family:"Times New
Roman","serif""><o:p></o:p></span></p>
<p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
line-height:18.0pt;tab-stops:324.0pt" align="center"><span
style="font-size:16.0pt;font-family:
"Times New Roman","serif"">ore <span
style="mso-no-proof:yes">16:00</span><o:p></o:p></span></p>
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line-height:18.0pt;tab-stops:324.0pt" align="center"><span
style="font-size:16.0pt;font-family:
"Times New Roman","serif""><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
line-height:18.0pt;tab-stops:324.0pt" align="center"><u><span
style="font-size:16.0pt;
font-family:"Times New Roman","serif"">Scuola
Normale Superiore<o:p></o:p></span></u></p>
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line-height:18.0pt;tab-stops:324.0pt" align="center"><span
style="font-size:16.0pt;font-family:
"Times New Roman","serif"">Pisa<o:p></o:p></span></p>
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line-height:18.0pt;tab-stops:324.0pt" align="center"><span
style="font-size:16.0pt;font-family:
"Times New Roman","serif"">Aula <span
style="mso-no-proof:yes">Mancini</span><o:p></o:p></span></p>
<p class="MsoNormal" style="tab-stops:324.0pt"><b><u><span
style="font-size:10.0pt;
font-family:"Times New Roman","serif""><o:p><span
style="text-decoration:none"> </span></o:p></span></u></b></p>
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style="font-size:10.0pt;
font-family:"Times New Roman","serif""><o:p><span
style="text-decoration:none"> </span></o:p></span></u></b></p>
<pre style="text-align:center"><b style="mso-bidi-font-weight:normal"><span style="font-size:22.0pt;font-family:"Times New Roman","serif"">Dr. Lars Khuene<o:p></o:p></span></b></pre>
<pre style="text-align:center"><span style="font-size:12.0pt;font-family:"Times New Roman","serif"">(SNS)<o:p></o:p></span></pre>
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normal"><i style="mso-bidi-font-style:normal"><span
style="font-family:"Times New
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mso-no-proof:yes"><o:p> </o:p></span></i></b></p>
<p class="MsoNormal" style="text-align:center;tab-stops:324.0pt"
align="center"><span
style="font-size:16.0pt;font-family:"Times New
Roman","serif"">Terrà un
seminario dal titolo:<o:p></o:p></span></p>
<p class="MsoNormal" style="tab-stops:324.0pt"><span
style="font-family:"Times New
Roman","serif""><o:p> </o:p></span></p>
<p class="MsoNormal" style="tab-stops:324.0pt"><span
style="font-size:10.0pt;
font-family:"Times New Roman","serif""><o:p> </o:p></span></p>
<pre style="text-align:center"><b style="mso-bidi-font-weight:normal"><i style="mso-bidi-font-style:normal"><span style="font-size:22.0pt;
font-family:"Times New Roman","serif";mso-ansi-language:EN-US" lang="EN-US">“</span></i></b><b style="mso-bidi-font-weight:normal"><span style="font-size:22.0pt;
font-family:"Times New Roman","serif";mso-ansi-language:EN-US" lang="EN-US">Logarithms of Algebraic Numbers<i style="mso-bidi-font-style:normal">”</i><o:p></o:p></span></b></pre>
<p class="MsoNormal" style="text-align:center" align="center"><b
style="mso-bidi-font-weight:
normal"><i style="mso-bidi-font-style:normal"><span
style="font-size:22.0pt;font-family:"Times New
Roman","serif";mso-ansi-language:
EN-US" lang="EN-US"><o:p> </o:p></span></i></b></p>
<p class="MsoNormal" style="text-align:justify"><b
style="mso-bidi-font-weight:
normal"><i style="mso-bidi-font-style:normal"><span
style="font-family:"Times New
Roman","serif";mso-ansi-language:EN-US"
lang="EN-US">Abstract:<o:p></o:p></span></i></b></p>
<pre style="text-align:justify"><i style="mso-bidi-font-style:normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif";
mso-ansi-language:EN-US" lang="EN-US">In my talk, I will discuss a variation of a method developed (by P. Débes and Y. André) in the context of G-functions. To be precise, this variation yields transcendence measures related with the one-dimensional multiplicative torus G_m.
Up to now, using the same method the transcendence of G-function values has been only obtained in a few cases (Y. André, "G-fonctions et transcendence", Crelle 1996) closely related with the modular curve X(2) and the associated hypergeometric functions.
In the talk, I present my humble effort to translate a part of André's work to the multiplicative torus G_m, obtaining various transcendence measures for logarithms.<o:p></o:p></span></i></pre>
<pre style="text-align:justify"><i style="mso-bidi-font-style:normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif";
mso-ansi-language:EN-US" lang="EN-US">It turns out that the analogue of André's proof is closely related to the classical proofs of certain transcendence measures of logarithms, the most prominent of which is the one given by K. Mahler ("On the approximation of logarithms of algebraic numbers", 1952).
In fact, Padé approximations to the logarithm (and its multiples) play a major role. However, the Padé approximations used in the approach presented comes not from any ingenious adhoc inspection but straight from Siegel's lemma.
An additional difference is the fact that I have to work with Padé approximations to the logarithm at a certain (varying) set of roots of unity instead of the unity (= 1) of G_m itself.<o:p></o:p></span></i></pre>
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lang="EN-US"><o:p> </o:p></span></i></b></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-size:16.0pt;
font-family:"Times New Roman","serif"">Tutti
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partecipare.<o:p></o:p></span></p>
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Classe di Scienze<o:p></o:p></span></p>
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<pre class="moz-signature" cols="72">--
--------------------------------------------------------------------------------
Valeria Giuliani
Scuola Normale Superiore
Servizio alla Didattica e Allievi
Tel. 050-509260
Piazza dei Cavalieri, 7
56126 Pisa
E-Mail: <a class="moz-txt-link-abbreviated" href="mailto:v.giuliani@sns.it">v.giuliani@sns.it</a>
E-Mail: <a class="moz-txt-link-abbreviated" href="mailto:adi.sd@sns.it">adi.sd@sns.it</a>
Le informazioni contenute nella presente e-mail e nei relativi allegati possono essere riservate e sono, comunque, destinate esclusivamente al destinatario in indirizzo.
E’ vietata, pertanto, la diffusione, distribuzione e/o copiatura di tali informazioni da parte di qualsiasi soggetto diverso dal destinatario.
Chiunque abbia ricevuto o letto questa e-mail per errore o senza esserne legittimato è invitato a darne immediatamente notizia al mittente tramite fax o e-mail e a distruggerla.
Grazie.
</pre>
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