Abstract
Let q be a sufficiently large integer and χ be a Dirichlet character modulo q. In this paper, we extend the product Πχ(−1)=−1 L(1, χ) with prime q, arising from the Kummer conjecture, to the products of some general Dirichlet series, and give some meaningful estimates for them.
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Feng, K. Q.: On the first factor of the class number of a cyclotomic field. Proc. Math. Ame. Soc., 84, 479–482 (1982)
Feng, K. Q.: Introduction to Algebraic Number Theory, Shanghai Science & Technology Press, Shanghai, 1988
Montgomery, H. L., Vaughan, R. C.: The large sieve. Mathematika, 20, 119–134 (1973)
Murty, M. R., Petridis, Y. N.: On Kummer’s conjecture. J. Number Theory, 90, 294–303 (2001)
Granville, A.: On the size of the first factor of the class number of a cyclotomic field. Invent. Math., 100, 321–338 (1990)
Lu, Y. M., Zhang, W. P.: On the Kummer conjecture. Acta Arith., 131(1), 87–102 (2008)
Bateman, P. T., Chowla, S., Erdös, P.: Remarks on the size of L(1, χ). Publ. Math. Debrecen, 1, 165–182 (1950)
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Supported by National Natural Science Foundation of China (Grant No. 10601039)
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Zhang, J.H., Yi, Y. & Xi, P. On the products arising from the Kummer conjecture. Acta. Math. Sin.-English Ser. 28, 1677–1688 (2012). https://doi.org/10.1007/s10114-012-9491-x
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DOI: https://doi.org/10.1007/s10114-012-9491-x