Averages of values of series
Author:
Emre Alkan
Journal:
Proc. Amer. Math. Soc. 141 (2013), 11611175
MSC (2010):
Primary 11M06, 11L05
Published electronically:
August 28, 2012
Fulltext PDF
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Abstract: We obtain an exact formula for the average of values of series over two independent odd characters. The average of any positive moment of values at 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 series at 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
Email:
ealkan@ku.edu.tr
DOI:
http://dx.doi.org/10.1090/S000299392012115060
PII:
S 00029939(2012)115060
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, TübaGebip 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.
