Quadratic Congruences
نویسنده
چکیده
1 Quadratic Congruences to Prime Moduli . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Quadratic Congruences to Composite Moduli . . . . . . . . . . . . . . . . . . . . . 5 3 Some Sums of Legendre’s symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
منابع مشابه
Inhomogeneous Quadratic Congruences
— For given positive integers a, b, q we investigate the density of solutions (x, y) ∈ Z to congruences ax+ by ≡ 0 mod q.
متن کاملMemoir on the General Theory of Surfaces And
CONTENTS Introduction. 79 1. Fundamental equations for a surface referred to its asymptotic curves. 85 2. Reciprocal congruences and the relation R. 86 3. The developables of the congruences T and r". 88 4. The focal points of the lines I and I'. 90 5. The directrix congruences. 91 6. Some general properties of reciprocal congruences. 93 7. The osculating quadric, and its connection-with recipr...
متن کاملSome New Series for 1/π and Related Congruences
In this paper we prove some new series for 1/π as well as related congruences. We also raise several new kinds of series for 1/π and present some related conjectural congruences involving representations of primes by binary quadratic forms.
متن کاملQuadratic Congruences for Cohen - Eisenstein Series
The notion of quadratic congruences was introduced in the recently appeared paper [1]. In this note we present another, somewhat more conceptual proof of several results from loc. cit. Our method allows to refine the notion and to generalize the results quoted. Here we deal only with the quadratic congruences for Cohen Eisenstein series. A similar phenomena exists for cusp forms of half-integra...
متن کاملCongruences Related to the Ankeny-artin-chowla Conjecture
Let p be an odd prime with p ⌘ 1 (mod 4) and " = (t + upp)/2 > 1 be the fundamental unit of the real quadratic field K = Q(pp) over the rationals. The Ankeny-Artin-Chowla conjecture asserts that p u, which still remains unsolved. In this paper, we investigate various kinds of congruences equivalent to its negation p | u by making use of Dirichlet’s class number formula, the products of quadrati...
متن کامل