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A simplified proof of this theorem was given by Rodosskii [7] whose proof (similar to Linnik's) rests basically on (A) functiontheoretic lemmas, (B) theorems on L-functions, (C) estimates of character sums, and (D) a sieve method. The theorems (B) can be classified and characterized as follows: (Bl) order of magnitude of the L-functions [5, Chapter 4, Satz 5.4], (B2) existence of at most one exceptional zero [5, Chapter 4, Satz 6.9], (B3) SiegeFs theorem on the exceptional zero [5, Chapter 4, Satz 8.1], (B4) functional equation of the L-functions [5, Chapter 7, Satz i . i ] , (B5) number of zeros in vertical strips [5, Chapter 7, Satz 3.3], (B6) explicit formulae [5, Chapter 7, Satz 4.1, Satz 6.1].

On the prime ideals of smallest norm in an ideal class \bmod𝔣 of an algebraic number field