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Averages of values of $ L$-series

Author: Emre Alkan
Journal: Proc. Amer. Math. Soc. 141 (2013), 1161-1175
MSC (2010): Primary 11M06, 11L05
Published electronically: August 28, 2012
MathSciNet review: 3008864
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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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Additional Information

Emre Alkan
Affiliation: Department of Mathematics, Koç University, Rumelifeneri Yolu, 34450, Sarıyer, Istanbul, Turkey

Keywords: $L$-series, special values, Jordan’s totient function, Euler’s totient function, averages, Gauss sums, cotangent sums
Received by editor(s): August 9, 2011
Received by editor(s) in revised form: August 15, 2011
Published electronically: August 28, 2012
Additional Notes: The author is supported by the Distinguished Young Scholar Award, Tüba-Gebip of Turkish Academy of Sciences
Dedicated: Dedicated to the memory of Professor Cemal Koç
Communicated by: Ken Ono
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.