7 citations · 22 across the 19 of their papers we have counts for
7 papers · 1 filter
The Sufficient Set of Congruences of Binomial Coefficients for Primality
Zubeyir Cinkir
For any given integer , we show that primality of is equivalent to congruences of binomial coefficients modulo . We also give extensi…
Beyond Wolstenholme's Theorem
Zubeyir Cinkir
Wolstenholme's type summations involve certain powers of all residues modulo some prime number . We first consider the sums of double or triple products of certain powers of…
An extension of Lucas Theorem
Zubeyir Cinkir, Aysegul Ozturkalan
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a prime. These criteria are analogues to the symmetry property of binomial coeffici…
Admissible Invariants of genus 3 Curves
Zubeyir Cinkir
Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we explicitly calculated these admissible invaria…
Explicit Computation of Certain Arakelov-Green Functions
Zubeyir Cinkir
Arakelov-Green functions defined on metrized graphs have important role in relating arithmetical problems on algebraic curves into graph theoretical problems. In this paper, we cla…
Computation of Polarized Metrized Graph Invariants By Using Discrete Laplacian Matrix
Zubeyir Cinkir
Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we give fast algorithms to compute these invarian…