Abstract
The Paley-Selberg asymptotic formula is refined to the form
where L(1∣χ)=\(\sum\limits_{n = 1}^\infty {\chi (n)n^{ - 1} } ,\left| \theta \right|< 10\), for a prime odd number p>35 and the summation is carried out over all nonprincipal characters χmodρ. As a consequence, upper estimates are obtained for the number of classes h of the field ℚ(exp2π/p) in the form h<20(πp/12)(p−2)/2, p>110.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 154, pp. 136–143, 1986.
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Slavutskii, I.S. Mean value of L-functions and the number of classes of a cyclotomic field. J Math Sci 43, 2596–2601 (1988). https://doi.org/10.1007/BF01374991
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DOI: https://doi.org/10.1007/BF01374991