Mathematics – Number Theory
Scientific paper
2009-06-15
Acta Arith. 150 (2011), 65-91
Mathematics
Number Theory
86 pages, Diplomarbeit, in German
Scientific paper
Let a and q be coprime natural numbers. In 1944 Linnik proved that the least prime in an arithmetic progression a mod q is less then C times q to the L. Since then the admissible value for the constant L has been improved several times, lastly by Heath-Brown in 1992 to L=5.5. In his article Heath-Brown describes several improvement potentials for his paper. Using these potentials we improve the intermediate results concerning zeros of Dirichlet L-Functions and finally the admissible constant to L=5.2. ----- Seien a und q teilerfremde natuerliche Zahlen. 1944 bewies Linnik, dass die kleinste Primzahl in einer arithmetischen Progression a mod q kleiner als C mal q hoch L ist. Seitdem wurde der zulaessige Wert fuer die Konstante L oft verbessert, zuletzt 1992 durch Heath-Brown auf L=5.5. In letzterem Artikel gibt Heath-Brown verschiedene Potentiale zur Verbesserung seiner Arbeit an. Mit diesen Potentialen verbessern wir die Zwischenresultate betreffend den Nullstellen von Dirichletschen L-Funktionen und schliesslich die zulaessige Konstante auf L=5.2.
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