The d-convex sets in a metric space are those subsets which include the metric interval between any two of its elements. Weak modularity is a certain interval property for triples of points. The d-convexity of a discrete weakly modular space X coincides with the geodesic convexity of the graph formed by the two-point intervals in X. The Helly number of such a space X turns out to be the same as...

We utilize effective algorithms for computing in the cohomology of a Shimura curve together with the Jacquet-Langlands correspondence to compute systems of Hecke eigenvalues associated to Hilbert modular forms over a totally real field F . The design of algorithms for the enumeration of automorphic forms has emerged as a major theme in computational arithmetic geometry. Extensive computations h...

In this work, we study the structure of multivariable modular codes over finite chain rings when the ambient space is a principal ideal ring. We also provide some applications to additive modular codes over the finite field $\mathbb{F}_4$.

Dedekind symbols generalize the classical Dedekind sums (symbols). The symbols are determined uniquely by their reciprocity laws up to an additive constant. There is a natural isomorphism between the space of Dedekind symbols with polynomial (Laurent polynomial) reciprocity laws and the space of cusp (modular) forms. In this article we introduce Hecke operators on the space of weighted Dedekind...

In this paper, we introduce $rho$-altering $J$-type mappings in modular spaces. We prove some fixed point theorems for $rho$-altering and $rho$-altering $J$-type mappings in modular spaces. We also furnish illustrative examples to express relationship between these mappings. As a consequence, the results are applied to the existence of solution of an integral equation arising from an ODE ...

For a prime p we describe an algorithm for computing the Brandt matrices giving the action of the Hecke operators on the space V of modular forms of weight 2 and level p2. For p ≡ 3 mod 4 we define a special Hecke stable subspace V0 of V which contains the space of modular forms with CM by the ring of integers of Q( √−p) and we describe the calculation of the corresponding Brandt matrices.

For a prime p we describe an algorithm for computing the Brandt matrices giving the action of the Hecke operators on the space V of modular forms of weight 2 and level p2. For p ≡ 3 mod 4 we define a special Hecke stable subspace V0 of V which contains the space of modular forms with CM by the ring of integers of Q( √−p) and we describe the calculation of the corresponding Brandt matrices.

This work presents a modular technique for minimizing a nite state machine FSM while preserving its equivalence to the original system Being modular the minimization technique should consume less time and space Preserving equivalence the resulting minimized model can be employed in both temporal logic model checking and sequential equivalence checking thus reducing their time and space consumpt...

The finite field modular multiplier is the most critical component in the elliptic curve crypto processor (ECCP) consuming the maximum chip area and contributing the most to the device latency. Modular multiplication, point multiplication, point doubling are few of the critical activities to be carried out by multiplier in ECC algorithm, and should be managed without compromising on security an...