Submission Deadline: 30 April 2023 (closed) View: 142
It is well known that number theory and combinatorics are two very important research branches of pure mathematics, many mathematical problems are closely related to them, such as Riemann hypothesis, Waring problem, Goldbach conjecture, twin prime conjecture, etc. Number theory and combinatorics is mainly concerned with numbers, thus many problems on these two fields can be converted or expressed by computable formulae. Because of this, computer tools are widely applied to these problems. To be concrete, computer tools help to verify the accuracy of conjectures, improve the error term of the estimations of inequalities, calculate the numerical results of computational formulae and so on. Therefore, it is necessary to conduct in-depth research in these fields, in order to make some progress in the study of certain mathematical theoretical problems. This special issue will focus on the contents of the study of number theory and combinatorics, especially those pure mathematical problems that can be realized with the help of computer tools. We will convert such mathematical problems into the forms suitable for computers to solve. Of course, we are not limited to these.
The aim of this special issue is to study various recurrence sequences, combinatorial identities and the calculation of the power mean of exponential sums and character sums, and to obtain some precise calculation formulae for them. Due to the computational complexity of such problems, we try to solve them by using mathematical modeling or computer programming, in order to achieve better results.
Potential topics include but are not limited to the following:
· Recurrence sequences
· Various exponential sums and their power mean
· Combinatorial identities
· Mathematical modeling
· Computer programming
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