Publication:
Averages of values of L-series

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Ono, Ken

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English

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Abstract

We obtain an exact formula for the average of values of L-series over two independent odd characters. The average of any positive moment of values at s = 1 is then expressed in terms of finite cotangent sums subject to congruence conditions. As consequences, bounds on such cotangent sums, limit points for the average of first moment of L-series at s = 1 and the average size of positive moments of character sums related to the class number are deduced.

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Proceedings of the American Mathematical Society

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American Mathematical Society (AMS)

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Mathematics, Applied mathematics

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