Determination of $∑_{k=1}^{p-1} g^{ak²}$ modulo p
نویسندگان
چکیده
منابع مشابه
On Hadamard Modulo Prime p Matrices of Size at most 2 p + 1 1
In this note, we continue the study of Hadamard Modulo Prime (HMP) matrices initialized in recent articles [5] – [6]. Namely, we have present some new non-existence and classification results for HMP matrices whose size is relatively small with respect to the modulo.
متن کاملSquare Roots Modulo p
The algorithm of Tonelli and Shanks for computing square roots modulo a prime number is the most used, and probably the fastest among the known algorithms when averaged over all prime numbers. However, for some particular prime numbers, there are other algorithms which are considerably faster. In this paper we compare the algorithm of Tonelli and Shanks with an algorithm based in quadratic fiel...
متن کاملDistribution of Residues Modulo p
The distribution of quadratic residues and non-residues modulo p has been of intrigue to the number theorists of the last several decades. Although Gauss’ celebrated Quadratic Reciprocity Law gives a beautiful criterion to decide whether a given number is a quadratic residue modulo p or not, it is still an open problem to find a small upper bound on the least quadratic non-residue mod p as a fu...
متن کاملProducts of Factorials Modulo p
The problem that we investigate in this note is the following: given p, find sufficient conditions that the parameters s and t should satisfy such as to ensure that Ps,t(p) contains the entire Zp. Let ε > 0 be any small number. Throughout this paper, we denote by c1, c2, . . . computable positive constants which are either absolute or depend on ε. From the way we formulated the above problem, w...
متن کاملSymmetric Pascal matrices modulo p
T = 1 1 1 1 2 1 1 3 3 1 .. . . . = exp 0 1 0 0 2 0 0 3 0 . . . with coefficients ti,j = (i j ) . This shows that det(P (n)) = 1 and that P (n) is positive definite for all n ∈ N. It implies furthermore that the characteristic polynomial det(tI(n)−P (n)) = ∑ k=0 αkt k (where I(n) denotes the identity matrix of order n) of P (n) has only positive real roots. The in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1992
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-61-2-161-172