✦ LIBER ✦

On a Problem of H. Cohn for Character Sums

✍ Scribed by Todd Cochrane; David Garth; Zhiyong Zheng

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 141 KB
Volume: 81
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1999.2457

No coin nor oath required. For personal study only.

✦ Synopsis

Cohn's problem on character sums (see , p. 202) asks whether a multiplicative character on a finite field can be characterized by a kind of two level autocorrelation property. Let f be a map from a finite field F to the complex plane such that f (0)=0, f (1)=1, and | f (:)| =1 for all :{0. In this paper we show that if for all a, b # F*, we have (q&1) :

then f is a multiplicative character of F. We also prove that if F is a prime field and f is a real valued function on F with f (0)=0, f (1)=1, and | f (:)| =1 for all :{0, then : # F f (:) f (:+a)=&1 for all a{0 if and only if f is the Legendre symbol.

These results partially answer Cohn's problem.

📜 SIMILAR VOLUMES

On a Character Sum Problem of Cohn

✍ Pär Kurlberg 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 92 KB

Let f be a complex-valued function on a finite field F such that f(0)=0, f(1)=1, and |f(x)|=1 for x ] 0. H. Cohn asked if it follows that f is a nontrivial multiplicative character provided that ; x ¥ F f(x) f(x+h)=-1 for h ] 0. We prove that this is the case for finite fields of prime cardinality u

Notes on a Problem of H. Cohn

✍ András Biró 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 103 KB

We prove some partial results concerning the following problem: Assume that F is a finite field, a i is a complex number for each i # F such that a 0 =0, a 1 =1, |a i | =1 for all i # F "[0], and i # F a i+j aÄ i =&1 for all i # F "[0]. Does it follow that the function i Ä a i is a multiplicative ch

Counter-examples to a Problem of Cohn on

Counter-examples to a Problem of Cohn on Classifying Characters

✍ Kwok-Kwong Choi; Man-Keung Siu 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 119 KB

On a problem of T. Kato

✍ H. Brezis 📂 Article 📅 1971 🏛 John Wiley and Sons 🌐 English ⚖ 214 KB

A Note on the Neumann Problem for a Quas

A Note on the Neumann Problem for a Quasilinear Elliptic Problem of a Nonmonotone Type

✍ Ivan Hlaváček 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 155 KB

The existence and uniqueness of a weak solution of a Neumann problem is discussed for a second-order quasilinear elliptic equation in a divergence form. The note is a continuation of a recent paper, where mixed boundary value problems were considered, which guaranteed the coerciveness of the problem

Effect of character attribution on Photo

Effect of character attribution on Photofit construction of a face

✍ J. W. Shepherd; H. D. Ellis; Mary McMurran; G. M. Davies 📂 Article 📅 1978 🏛 John Wiley and Sons 🌐 English ⚖ 323 KB