منابع مشابه
Infinite Global Fields and the Generalized Brauer–siegel Theorem
The paper has two purposes. First, we start to develop a theory of infinite global fields, i. e., of infinite algebraic extensions either of Q or of Fr(t). We produce a series of invariants of such fields, and we introduce and study a kind of zeta-function for them. Second, for sequences of number fields with growing discriminant, we prove generalizations of the Odlyzko–Serre bounds and of the ...
متن کاملGeneralized Euler constants 3
We study the distribution of a family {γ(P)} of generalized Euler constants arising from integers sieved by finite sets of primes P . For P = Pr, the set of the first r primes, γ(Pr)→ exp(−γ) as r →∞. Calculations suggest that γ(Pr) is monotonic in r, but we prove it is not. Also, we show a connection between the distribution of γ(Pr) − exp(−γ) and the Riemann hypothesis.
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We define a family {γ(P)} of generalized Euler constants indexed by finite sets of primes P and study their distribution. An apparent monotonicity is investigated.
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and when K is imaginary quadratic, the well-known Kronecker limit formula expresses γK in terms of special values of the Dedekind η function. This constant γK appears here and there in several articles in analytic number theory, but as far as the author knows, it has not played a main role nor has it been studied so systematically. We shall consider γK more as an invariant of K. Before explaini...
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Article history: Received 16 October 2008 Revised 11 June 2009 Communicated by David Goss MSC: primary 11J81 secondary 11J86, 11J91
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2019
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14793