On the Cotangent Sums Related to Estermann Zeta Function and Arithmetic Properties of their Arguments

In this work we are interested by cotangent sum related to Estermann zeta function in rational arguments. In the first place we look at the maximum and the moment as they did H. Maier and M. Th. Rassias in short interval and get some interesting new identities. Afterwards, based on some recent results, we study special cases where we provide the series expansion of this sum. We end the work by the associated arithmetical problem; which consists to find the relation between an integer and its inverse in congruence theory.

Tangible Self-Consequation and Arithmetical Problem-Solving: An Exploratory Comparison of Four Strategies

In an exploratory investigation, 25 volunteer postgraduate students were exposed to a control and four self-consequation conditions of positive and negative reward and positive and negative punishment. The experimental tasks were arithmetic problems matched for difficulty. Generally, the results indicated that, when subjects were operating under the two self-reward conditions whereby they self-reinforced correct responses, they attempted more items and produced more correct responses. Conversely, as predicted, participants in the two self-punishment conditions were more accurate.