AVERAGES OF VALUES OF L-SERIES

作者：Alkan Emre^*

来源：Proceedings of the American Mathematical Society, 2013, 141(4): 1161-1175.

• L-series
• special values
• Jordan's totient function
• Euler's totient function
• averages
• Gauss sums
• cotangent sums

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.

• 出版日期2013-4