Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Entire DC Network
Diagonal Forms And The Rationality Of The Poincaré Series, Dibyajyoti Deb
Diagonal Forms And The Rationality Of The Poincaré Series, Dibyajyoti Deb
University of Kentucky Doctoral Dissertations
The Poincaré series, Py(f) of a polynomial f was first introduced by Borevich and Shafarevich in [BS66], where they conjectured, that the series is always rational. Denef and Igusa independently proved this conjecture. However it is still of interest to explicitly compute the Poincaré series in special cases. In this direction several people looked at diagonal polynomials with restrictions on the coefficients or the exponents and computed its Poincaré series. However in this dissertation we consider a general diagonal polynomial without any restrictions and explicitly compute its Poincaré series, thus extending results of Goldman, Wang and Han. In a separate …
The Fibonacci Sequence, Arik Avagyan
The Fibonacci Sequence, Arik Avagyan
A with Honors Projects
A review was made of the Fibonacci sequence, its characteristics and applications.
Ergodic And Combinatorial Proofs Of Van Der Waerden's Theorem, Matthew Samuel Rothlisberger
Ergodic And Combinatorial Proofs Of Van Der Waerden's Theorem, Matthew Samuel Rothlisberger
CMC Senior Theses
Followed two different proofs of van der Waerden's theorem. Found that the two proofs yield important information about arithmetic progressions and the theorem. van der Waerden's theorem explains the occurrence of arithmetic progressions which can be used to explain such things as the Bible Code.