Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Institution
- Keyword
- Publication
- Publication Type
Articles 1 - 7 of 7
Full-Text Articles in Number Theory
Ramanujan-Like Congreuences Of The Distinct Partition Function, Ian Blumenfeld, Christi Carlstead, Mimi Cukier, Wesley Terway
Ramanujan-Like Congreuences Of The Distinct Partition Function, Ian Blumenfeld, Christi Carlstead, Mimi Cukier, Wesley Terway
Mathematical Sciences Technical Reports (MSTR)
In his work with the partition function, Ramanujan observed several congruences of the form p(An + B) = 0 (mod m). We adapt this form to several congruences of the distinct partition function, p2(n). We show that one can determine all ordered pairs of integers (A;B) for which p2(An + B)=0 (mod 2) and show families of congruences modulo 4. Finally, we offer a proof of a congruence modulo 5 satisfied by the distinct partition function.
Torsion-Free Modules Over Reduced Witt Rings, Robert W. Fitzgerald
Torsion-Free Modules Over Reduced Witt Rings, Robert W. Fitzgerald
Articles and Preprints
We compute the genus class group of a torsion-free module over a reduced Witt ring of finite stability index. This is applied to modules locally isomorphic to odd degree extensions of formally real fields.
Modular Symbols And Hecke Operators, Paul E. Gunnells
Modular Symbols And Hecke Operators, Paul E. Gunnells
Paul Gunnells
We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and Ash-Rudolph. Most of the work is contained in papers of the author and the author with Mark McConnell. Some results are unpublished work of Mark McConnell and Robert MacPherson.
Computing Special Values Of Partial Zeta Functions, Gautam Chinta, Paul E. Gunnells, Robert Sczech
Computing Special Values Of Partial Zeta Functions, Gautam Chinta, Paul E. Gunnells, Robert Sczech
Paul Gunnells
We discuss computation of the special values of partial zeta functions associated to totally real number fields. The main tool is the Eisenstein cocycle Ψ, a group cocycle for GL n (ℤ); the special values are computed as periods of Ψ, and are expressed in terms of generalized Dedekind sums. We conclude with some numerical examples for cubic and quartic fields of small discriminant.
The Proof Of Fermat's Last Theorem, Mohamad Trad
The Proof Of Fermat's Last Theorem, Mohamad Trad
Theses Digitization Project
Fermat, Pierre de, is perhaps the most famous number theorist who ever lived. Fermat's Last Theorem states that the equation xn + yn = zn has no non-zero integer solutions for x, y and z when n>2.
Algebra În Exercijii Şi Probleme Pentru Liceu, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin
Algebra În Exercijii Şi Probleme Pentru Liceu, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Definitions, Solved And Unsolved Problems, Conjectures, And Theorems In Number Theory And Geometry, Florentin Smarandache
Definitions, Solved And Unsolved Problems, Conjectures, And Theorems In Number Theory And Geometry, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Florentin Smarandache, an American mathematician of Romanian descent has generated a vast variety of mathematical problems. Some problems are easy, others medium, but many are interesting or unsolved and this is the reason why the present book appears. Here, of course, there are problems from various types. Solving these problems is addictive like eating pumpkin seed: having once started, one cannot help doing it over and over again.