On the Quadratic Character of a Polynomial

1967 ◽  
Vol s1-42 (1) ◽  
pp. 73-80 ◽  
Author(s):  
D. A. Burgess
Keyword(s):  
Quadratic Character

Weighted Measures of Pseudorandom Binary Lattices

2021 ◽  
Vol 58 (3) ◽  
pp. 319-334
Author(s):  
Huaning Liu ◽  
Yinyin Yang
Keyword(s):  
Finite Fields ◽  
Lower Bounds ◽  
Binary Sequences ◽  
Quadratic Character ◽  
Pseudorandom Sequences ◽  
Even Order

In cryptography one needs pseudorandom sequences whose short subsequences are also pseudorandom. To handle this problem, Dartyge, Gyarmati and Sárközy introduced weighted measures of pseudorandomness of binary sequences. In this paper we continue the research in this direction. We introduce weighted pseudorandom measure for multidimensional binary lattices and estimate weighted pseudorandom measure for truly random binary lattices. We also give lower bounds for weighted measures of even order and present an example by using the quadratic character of finite fields.

Heights and L-Series

1990 ◽  
Vol 42 (3) ◽  
pp. 533-560 ◽  
Author(s):  
Rhonda Lee Hatcher
Keyword(s):  
Dirichlet Series ◽  
Cusp Form ◽  
Quadratic Field ◽  
Imaginary Quadratic Field ◽  
Ideal Class ◽  
Quadratic Character ◽  
Trivial Character ◽  
Image Position

Let be a cusp form of weight 2k and trivial character for Γ0(N), where N is prime, which is orthogonal with respect to the Petersson product to all forms g(dz), where g is of level L < N, dL\N. Let K be an imaginary quadratic field of discriminant — D where the prime N is inert. Denote by ∊ the quadratic character of determined by ∊(p) = (—D/p) for primes p not dividing D. For A an ideal class in K, let rA(m) be the number of integral ideals of norm m in A. We will be interested in the Dirichlet series L(f,A,s) defined by

The Quadratic Character of 2 mod p

1976 ◽  
Vol 49 (2) ◽  
pp. 89-90
Author(s):  
Kenneth S. Williams
Keyword(s):  
Quadratic Character ◽  
Mod P

scholarly journals Modular forms of half-integral weights on SL(2, ℤ)

2014 ◽  
Vol 215 ◽  
pp. 1-66
Author(s):  
Yifan Yang
Keyword(s):  
Modular Forms ◽  
Analogous Result ◽  
Quadratic Character ◽  
Hecke Modules ◽  
Shimura Correspondence

AbstractIn this paper, we prove that, for an integerrwith (r, 6) = 1 and 0&lt; r &lt;24 and a nonnegative even integers, the setis isomorphic toas Hecke modules under the Shimura correspondence. HereMs(1) denotes the space of modular forms of weightis the space of newforms of weight 2kon Γ0(6) that are eigenfunctions with eigenvalues€2and€3for Atkin-Lehner involutionsW2andW3, respectively, and the notation ⊕(12/.) means the twist by the quadratic character (12/-). There is also an analogous result for the cases (r, 6) = 3.

Quartic residuacity and the quadratic character of certain quadratic irrationalities

2015 ◽  
Vol 11 (08) ◽  
pp. 2487-2503
Author(s):  
Ronald J. Evans ◽  
Kenneth S. Williams
Keyword(s):  
Quadratic Form ◽  
General Theorem ◽  
Binary Quadratic Form ◽  
Legendre Symbol ◽  
Quadratic Character

We prove a general theorem that evaluates the Legendre symbol [Formula: see text] under certain conditions on the integers A, B, m and the prime p. The evaluation is in terms of parameters appearing in a binary quadratic form representing p. The theorem has applications to quartic residuacity.

Quadratic and higher reciprocity of modular polynomials

1944 ◽  
Vol 40 (3) ◽  
pp. 212-214 ◽  
Author(s):  
H. C. Pocklington
Keyword(s):  
Quadratic Character ◽  
Modular Polynomials

1. We first compare the λ-ic characters of two polynomials with respect to each other and the prime p, the polynomials being irreducible with respect to p. This is done by relating each to the resultant of the polynomials. We then show in § 6 that the ordinary quadratic character of one prime with respect to another is also the resultant of two polynomials.

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