siegel zeros
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2016 ◽  
Vol 12 (08) ◽  
pp. 2201-2229 ◽  
Author(s):  
Asif Zaman

Let [Formula: see text] be a number field, [Formula: see text] be an integral ideal, and [Formula: see text] be the associated narrow ray class group. Suppose [Formula: see text] possesses a real exceptional character [Formula: see text], possibly principal, with a Siegel zero [Formula: see text]. For [Formula: see text] satisfying [Formula: see text] [Formula: see text], we establish an effective [Formula: see text]-uniform Linnik-type bound with explicit exponents for the least norm of a prime ideal [Formula: see text]. A special case of this result is a bound for the least rational prime represented by certain binary quadratic forms.


2015 ◽  
Vol 55 (3) ◽  
pp. 331-342
Author(s):  
Jean-Marie De Koninck ◽  
László Germán ◽  
Imre Kátai

2008 ◽  
Vol 04 (01) ◽  
pp. 45-56 ◽  
Author(s):  
EMMANUEL KNAFO

Through a refinement for the estimation of the effect of Siegel zeros, we show how to avoid the use of Siegel's theorem in order to obtain the first effective lower bound for the variance of distribution of primes in arithmetic progressions.


2007 ◽  
Vol 126 (4) ◽  
pp. 341-356
Author(s):  
Joseph Hundley

2002 ◽  
Vol 111 (3) ◽  
pp. 495-507 ◽  
Author(s):  
A. Zaharescu ◽  
P. Sarnak
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