A Refinement of the Hammer-mortenson Congruence

نویسندگان

  • Zhi-Wei Sun
  • ZHI-WEI SUN
چکیده

Let p be an odd prime. In 2008 E. Mortenson proved van Hamme's following conjecture: (p−1)/2 k=0 (4k + 1) −1/2 k 3 ≡ (−1) (p−1)/2 p (mod p 3).

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Refinement of the Hamme-mortenson Congruence

Let p be an odd prime. In 2008 E. Mortenson proved van Hamme's following conjecture: (p−1)/2 k=0 (4k + 1) −1/2 k 3 ≡ (−1) (p−1)/2 p (mod p 3).

متن کامل

On the Broken 1-diamond Partition

Abstract. We introduce a crank-like statistic for a different class of partitions. In [AP], Andrews and Paule initiated the study of broken k-diamond partitions. Their study of the respective generating functions led to an infinite family of modular forms, about which they were able to produce interesting arithmetic theorems and conjectures for the related partition functions. Here we establish...

متن کامل

A Refinement Theory for Concurrent Object Oriented Languages

A notion of refinement for concurrent object-oriented programs was originally presented in [3]. ln th.is article we prove that the refinement relation associated to this notion is a congruence with respect to various standard programming language constructors, including parallel and sequential composition, conditionals, and nondeterministic internal choice. We also establish a weaker compositio...

متن کامل

Hierarchical Meshes for Volume Data

An algorithm for adaptive refinement of 3D-meshes is outlined. This algorithm is very convenient for the generation of mesh hierarchies used for efficient volume visualization algorithms, e.g. iso-surface extraction or direct volume rendering, and for multilevel finite element computations. The aim was to construct an algorithm which generates as little congruence classes as possible. The main ...

متن کامل

A Uniform Refinement Property for Congruence Lattices

The Congruence Lattice Problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of a lattice. It was hoped that a positive solution would follow from E. T. Schmidt’s construction or from the approach of P. Pudlák, M. Tischendorf, and J. Tůma. In a previous paper, we constructed a distributive algebraic lattice A with א2 compact elements that cannot be ob...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010