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Majid-Ghandali/README.md

Python Field

Hi, I'm Majid πŸ‘‹

PhD Researcher in Mathematics

Exploring structural symmetries in recursive systems β€” Pure Mathematics at Computational Scale.

πŸ”¬ Research Focus

  • Computational Number Theory: Fibonacci modulo structures, elliptic curves & modular phenomena.
  • Arithmetic Dynamics: Fibonacci orbits over finite fields $\mathbb{F}_p$.
  • Prime Distribution: Structural corrections in prime-gap models.
  • Recursive Models: Higher-order Pisano period analysis.

🧠 Current Work

  • Developing corrected structural models for prime distribution.
  • Investigating structural relationships between Legendre sums ($S_p$) and Frobenius traces ($a_p$).
  • Building high-performance computational frameworks for large-scale arithmetic analysis.

πŸ“‚ Featured Projects

  • πŸš€ Fibonacci-Prime-Analysis
  • πŸ“‰ Prime-Decomposition
  • πŸ“ Pisano-Correction

βš™οΈ Tools & Stack

Python | SageMath | NumPy | SymPy | HPC Computing | LaTeX

🌱 Research Interests

  • Elliptic Cohomology & Galois Representations
  • Arithmetic Topology
  • Large-Scale Computational Mathematics

πŸ“« Contact

Popular repositories Loading

  1. fibonacci-character-sum-full-rank fibonacci-character-sum-full-rank Public

    Reproducibility code for "An Explicit Evaluation of a Fibonacci Character Sum for Primes with Full Rank of Apparition" β€” closed-form sign evaluation via primitive-root parametrization.

    Python 2

  2. fibonacci-cm-elliptic fibonacci-cm-elliptic Public

    Numerical verification of the identity S_p = -a_p(E) linking Fibonacci character sums and CM elliptic curves. DOI: 10.5281/zenodo.18764803

    TeX 1

  3. half-period-involutions-in-inert-lucas-sequences half-period-involutions-in-inert-lucas-sequences Public

    Reproducibility code for "Half-Period Involutions in Inert Lucas Sequences" β€” fixed-point-free half-period pairing and exact cancellation over inert Lucas sequences mod p.

    1

  4. Majid-Ghandali Majid-Ghandali Public

    Introduction

  5. fibchar-rank-blocks fibchar-rank-blocks Public template

    Reproducibility materials for Fibonacci character sums, scalar collapse, and rank-block decomposition.

    Python

  6. fibonacci-even-rank-reflection-selection fibonacci-even-rank-reflection-selection Public

    Reproducibility code for "Character-Twisted Reflection in Even-Rank Fibonacci Blocks" β€” index-dependent weighted reflection with a surviving midpoint fixed point.