Abstract
An asymptotic behavior of the sum
for X → ∞ is studied in the critical strip, where L(s, Xp) is the Dirichlet series with the quadratic character Xp modulo p, where p is a prime number; v=1 or 3. With the help of large seive estimates a formula for this sum is obtained with two asymptotic terms on the critical line of the variable s. As a corollary the asymptotic expansion of this sum at the point s=1/2 is presented. The asymptotic formula for the sum
, where d runs over discriminants of quadratic fields, is also obtained.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 109, pp. 41–82, 1981.
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Vinogradov, A.I., Takhtadzhyan, L.A. Analogues of the Gauss-Vinogradov formula on the critical line. J Math Sci 24, 183–208 (1984). https://doi.org/10.1007/BF01087241
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DOI: https://doi.org/10.1007/BF01087241