[DissKoll] DissKoll, June 18, 2009 , Victor Cuauhtemoc Garcia

[Klemens Katterbauer]

Dear visitors of the DissKoll (Dissertantenkolloquium),

On June 18, 2009, the DissKoll will have its last talk in spring 2009.
 Victor Cuauhtemoc Garcia (University of Natural Resources and Applied
Life Sciences, Vienna) will talk about "Additive properties of the
Ramanujan tau function" (joint work with M. Garaev and S. Konyagin).


Victor Cuauhtemoc Garcia
"Additive properties of the Ramanujan tau function" (joint work with
M. Garaev and S. Konyagin)

Abstract:
In this talk, after a brief introduction, I am planing to show how
arithmetic properties of the Ramanujan tau function $\tau(n)$ can be
combined with the Waring-Goldbach problem to prove that the set of the
values $\tau(n)$ forms a finite additive basis for the set of
integers. Moreover, for every integer $|N|\ge 2$, the Diophantine
equation $$ \tau(n_1)+ \ldots + \tau(n_{148000})=N, $$ has a solution
in positive integers $n_1, \ldots, n_{148000},$ satisfying the
condition $$ \max_{1\le i \le 148000}n_i \ll |N|^{2/11}e^{-c \log
|N|/\log \log|N|}, $$ for some absolute constant $c >0.$ In view of a
result of Deligne, this result reflects the best possible order of the
integers $n_i,$ apart from the value of the constant $c.$


Thursday, June 18, 2009, 17:15, Room C 2.09
Coffee and cakes served from 17:00 in the Common Room C 2.06

Program and further information you can find at
http://www.mat.univie.ac.at/~disskoll/

If you are interested in giving a talk, then please contact Klemens
Katterbauer via the below given E-mail address or cell phone number.

To join the mailing list, visit
http://www.mat.univie.ac.at/mailman/listinfo/disskoll

Comments and feedback are welcomed.

We are looking forward to your attendance,

 Victor Cuauhtemoc Garcia
Clemens Hanel
Klemens Katterbauer

+++++++++++++++++++++++++++++++++++++++++++++++++++

Liebe Besucherinnen und Besucher des DissKoll(Dissertantenkolloquium)!

Am Donnerstag den 4. Juni 2009 findet der letzte Vortrag im Rahmen des
DissKoll in diesem Semester statt. Victor Cuauhtemoc Garcia
(Universität für Bodenkultur, Institut für Mathematik) spricht über
"Additive properties of the Ramanujan tau function"

Victor Cuauhtemoc Garcia
"Additive properties of the Ramanujan tau function" (joint work with
M. Garaev and S. Konyagin)

Abstract:
In this talk, after a brief introduction, I am planing to show how
arithmetic properties of the Ramanujan tau function $\tau(n)$ can be
combined with the Waring-Goldbach problem to prove that the set of the
values $\tau(n)$ forms a finite additive basis for the set of
integers. Moreover, for every integer $|N|\ge 2$, the Diophantine
equation $$ \tau(n_1)+ \ldots + \tau(n_{148000})=N, $$ has a solution
in positive integers $n_1, \ldots, n_{148000},$ satisfying the
condition $$ \max_{1\le i \le 148000}n_i \ll |N|^{2/11}e^{-c \log
|N|/\log \log|N|}, $$ for some absolute constant $c >0.$ In view of a
result of Deligne, this result reflects the best possible order of the
integers $n_i,$ apart from the value of the constant $c.$


Donnerstag, 18. Juni 2009, 17:15, Seminarraum C 2.09
Kaffee und Kuchen ab 17:00 im Common Room C 2.06

Wir freuen uns auf euer Kommen,

Victor Cuauhtemoc Garcia
Clemens Hanel
Klemens Katterbauer


Das weitere Programm für dieses Semester findet ihr auf
http://www.mat.univie.ac.at/~disskoll/