We prove the analog of Cramér's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann hypothesis. Both results are uniform in the data of the underlying structure. Our approach is based mainly on the inertia property of the counting functions of primes and prime ideals.
Primes and prime ideals in short intervals / L. Grenié, G. Molteni, A. Perelli. - In: MATHEMATIKA. - ISSN 0025-5793. - 63:2(2017 Jan), pp. 364-371. [10.1112/S0025579316000310]
Primes and prime ideals in short intervals
G. Molteni;
2017
Abstract
We prove the analog of Cramér's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann hypothesis. Both results are uniform in the data of the underlying structure. Our approach is based mainly on the inertia property of the counting functions of primes and prime ideals.
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