Abstract. Bringmann and Lovejoy introduced a rank for overpartition pairs and investigated its role in congruence properties of pp(n), the number of overpartition pairs of n. In particular, they applied the theory of Klein forms to show that there exist many Ramanujan-type congruences for pp(n). In this paper, we derive two Ramanujantype identities and some explicit congruences for pp(n). Moreo...

An identity-based non-interactive public key distribution system is presented that is based on a novel trapdoor one-way function allowing a trusted authority to compute the discrete logarithms modulo a publicly known composite number m while this is infeasible for an adversary not knowing the factorization of m. Without interaction with a key distribution center or with the recipient of a given...

We establish two binomial coefficient–generalized harmonic sum identities using the partial fraction decomposition method. These identities are a key ingredient in the proofs of numerous supercongruences. In particular, in other works of the author, they are used to establish modulo p (k > 1) congruences between truncated generalized hypergeometric series, and a function which extends Greene’s ...

If E is an elliptic curve over Q, then let E(D) denote the D−quadratic twist of E. It is conjectured that there are infinitely many primes p for which E(p) has rank 0, and that there are infinitely many primes ` for which E(`) has positive rank. For some special curves E we show that there is a set S of primes p with density 1 3 for which if D = Q pj is a squarefree integer where pj ∈ S, then E...

We will use commutators to provide decompositions of 3×3 matrices as sums whose terms satisfy some polynomial identities, and we apply them bounded linear operators endomorphisms free modules infinite rank. In particular it is proved that every operator an infinite-dimensional complex Hilbert space a sum four automorphisms order 3 simple ring obtained quotient the endomorphism vector modulo its...

In this paper we characterize the matrices A with the following property: for each ε > 0 there exists k ∈ N such that ‖Ak − I‖ < ε for a given matrix norm. This characterization is applied to the theory of unitary, hermitian nonnegative, positive and stochastic matrices.

In this paper we show that if K is an incline with multiplicative identity and I is an r-ideal of K containing a unit u, then I = K. Moreover, we show that in a non-zero incline K with multiplicative identity and zero element, every proper r-ideal in K is contained in a maximal r-ideal of K. Z. Q. Cao, K. H. Kim and F. W. Roush [3] introduced the notion of incline algebras in their book, Inclin...

Rewriting with rules R modulo axioms E is a widely used technique in both rule-based programming languages and in automated deduction. Termination methods for rewriting systems modulo specific axioms E (e.g., associativity-commutativity) are known. However, much less seems to be known about termination methods that can be modular in the set E of axioms. In fact, current termination tools and pr...

We give new proofs of two basic results in number theory: The law of quadratic reciprocity and the sign of the Gauss sum. We show that these results are encoded in the relation between the discrete Fourier transform and the action of the Weyl element in the Weil representation modulo p, q and pq. 0. Introduction Two basic results due to Gauss are the quadratic reciprocity law and the sign of th...

Exp-log functions are those obtained from the constant 1 and the variable X by means of arithmetic operations and the function symbols exp() and logll. This paper gives an explicit algorithm for determining eventual dominance of these functions modulo an oracle for deciding zero equivalence of constant terms. This also provides another proof that the dominance problem for exp-log functions is T...