scholarly journals On some determinants with Legendre symbol entries

2019 ◽  
Vol 56 ◽  
pp. 285-307 ◽  
Author(s):  
Zhi-Wei Sun
Keyword(s):  
Legendre Symbol

scholarly journals Determinants of Legendre symbol matrices

2004 ◽  
Vol 115 (3) ◽  
pp. 231-244 ◽  
Author(s):  
Robin Chapman
Keyword(s):  
Legendre Symbol

Estimate of a multiple sum involving the legendre symbol

1975 ◽  
Vol 18 (3) ◽  
pp. 840-844 ◽  
Author(s):  
G. I. Perel'muter
Keyword(s):  
Legendre Symbol

scholarly journals Some Identities on the Character Sum Containing x(x - 1)(x - λ)

1971 ◽  
Vol 42 ◽  
pp. 109-113 ◽  
Author(s):  
Masatoshi Yamauchi
Keyword(s):  
Character Sum ◽  
Legendre Symbol ◽  
Prime Field

Let Fp be the prime field of characteristic p (p: an odd prime), and put = Fp - {0, 1}. Then for λ ∈ we define,where denotes the Legendre symbol, and consider the sum

scholarly journals A Bertrand postulate for a subclass of primes

2013 ◽  
Vol 31 (2) ◽  
pp. 109 ◽  
Author(s):  
G. Sudhaamsh Mohan Reddy ◽  
S. Srinivas Rau ◽  
Bidarahalli Uma
Keyword(s):  
Legendre Symbol ◽  
Squarefree Integer

Let d be a squarefree integer and consider the subclass of primes with Legendre symbol ( d/p ) = +1. It is shown that for x large enough (x; 2x] contain a prime of this type.

scholarly journals A Sum Connected with Quadratic Residues

1956 ◽  
Vol 10 ◽  
pp. 1-7
Author(s):  
L. Carlitz
Keyword(s):  
Positive Integer ◽  
Legendre Symbol ◽  
Arbitrary Positive Integer ◽  
Arbitrary Integer ◽  
Quadratic Residues

Let p be a prime > 2 and m an arbitrary positive integer; definewhere (r/p) is the Legendre symbol. We consider the problem of finding the highest power of p dividing Sm. A little more generally, if we putwhere a is an arbitrary integer, we seek the highest power of p dividing Sm(a). Clearly Sm = Sm(0), and Sm(a) = Sm(b) when a ≡ b (mod p).

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