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1.
Let p be a large prime number, K, L, M, λ be integers with 1 ≤ M ≤ p and gcd(λ, p) = 1. The aim of our paper is to obtain sharp upper bound estimates for the number I
2(M; K, L) of solutions of the congruence
xy o l (mod p), K+ 1 £ x £ K +M, L+ 1 £ y £ L +M,xy \equiv \lambda \quad ({\rm mod} p), \quad K+ 1 \leq x \leq K +M,\quad L+ 1 \leq y \leq L +M, 相似文献
2.
Harald Woracek 《Monatshefte für Mathematik》2012,33(3):105-149
A string is a pair (L, \mathfrakm){(L, \mathfrak{m})} where L ? [0, ¥]{L \in[0, \infty]} and \mathfrakm{\mathfrak{m}} is a positive, possibly unbounded, Borel measure supported on [0, L]; we think of L as the length of the string and of \mathfrakm{\mathfrak{m}} as its mass density. To each string a differential operator acting in the space L2(\mathfrakm){L^2(\mathfrak{m})} is associated. Namely, the Kreĭn–Feller differential operator -D\mathfrakmDx{-D_{\mathfrak{m}}D_x} ; its eigenvalue equation can be written, e.g., as
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