A 6 Integers 15 a ( 2015 ) on Reducible and Primitive Subsets of F P , I

نویسندگان

  • Katalin Gyarmati
  • András Sárközy
چکیده

A set A ⇢ Fp is said to be reducible if it can be represented in the form A = B+ C with B, C ⇢ Fp, |B| , |C| 2. If there are no sets B, C with these properties then A is said to be primitive. First three criteria are presented for primitivity of subsets of Fp. Then the distance between a given set A ⇢ Fp and the closest primitive set is studied. –Dedicated to the memory of Paul Erdős on the occasion of the 100th anniversary of his birthday.

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

EEH: AGGH-like public key cryptosystem over the eisenstein integers using polynomial representations

GGH class of public-key cryptosystems relies on computational problems based on the closest vector problem (CVP) in lattices for their security. The subject of lattice based cryptography is very active and there have recently been new ideas that revolutionized the field. We present EEH, a GGH-Like public key cryptosystem based on the Eisenstein integers Z [ζ3] where ζ3 is a primitive...

متن کامل

Some results on functionally convex sets in real Banach spaces

‎We use of two notions functionally convex (briefly‎, ‎F--convex) and functionally closed (briefly‎, ‎F--closed) in functional analysis and obtain more results‎. ‎We show that if $lbrace A_{alpha} rbrace _{alpha in I}$ is a family $F$--convex subsets with non empty intersection of a Banach space $X$‎, ‎then $bigcup_{alphain I}A_{alpha}$ is F--convex‎. ‎Moreover‎, ‎we introduce new definition o...

متن کامل

Ten new primitive binary trinomials

We exhibit ten new primitive trinomials over GF(2) of record degrees 24 036 583, 25 964 951, 30 402 457, and 32 582 657. This completes the search for the currently known Mersenne prime exponents. Primitive trinomials of degree up to 6 972 593 were previously known [4]. We have completed a search for all known Mersenne prime exponents [7]. Ten new primitive trinomials were found. Our results ar...

متن کامل

A NORM INEQUALITY FOR CHEBYSHEV CENTRES

In this paper, we study the Chebyshev centres of bounded subsets of normed spaces and obtain a norm inequality for relative centres. In particular, we prove that if T is a remotal subset of an inner product space H, and F is a star-shaped set at a relative Chebyshev centre c of T with respect to F, then llx - qT (x)1I2 2 Ilx-cll2 + Ilc-qT (c) 112 x E F, where qT : F + T is any choice functi...

متن کامل

Self-intersection of Dualizing Sheaves of Arithmetic Surfaces with Reducible Fibers

Let K be an algebraic number field and OK the ring of integers of K. Let f : X → Spec(OK) be a stable arithmetic surface over OK of genus g ≥ 2. In this short note, we will prove that if f has a reducible geometric fiber, then (ωAr X/OK · ωAr X/OK ) ≥ log 2/6(g − 1). Let K be a number field and OK the ring of integers of K. Let f : X → Spec(OK) be a stable arithmetic surface of genus g ≥ 2. One...

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 2015