The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory. The rational numbers are the most familiar numbers: 1, -5, ½, and every ...

Abstract In this paper we give some interesting equation of p-adic q-integrals on ℤp. From those p-adic q-integrals, we present a systemic study of some families of extended Carlitz q-Bernoulli ...

Let F be the function field of a smooth curve over the p-adic number field ℚp. We show that for each prime-to-p number n the n-torsion subgroup H2(F, μn) = n Br(F) is generated by ℤ/n-cyclic classes; ...

Arithmetic geometry of curves stands at the crossroads of algebraic geometry and number theory, offering a rigorous framework for analysing algebraic curves defined over number and finite fields. This ...