3 citations · 4 across the 4 of their papers we have counts for
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Arithmetic differential operators on Z_p
A. Buium, C. C. Ralph, S. R. Simanca
We prove that a function f from Z_p to itself is analytic if and only if it can be represented as f(x)=F(x, dx, ..., d^r x) where dx=(x-x^p)/p is the Fermat quotient operator and F…
Arithmetic Laplacians
Alexandru Buium, Santiago R. Simanca
We develop an arithmetic analogue of elliptic partial differential equations. The role of the space coordinates is played by a family of primes, and that of the space derivatives a…
Arithmetic partial differential equations, II: modular curves
Alexandru Buium, Santiago R. Simanca
We classify ``arithmetic convection equations'' on modular curves, and describe their space of solutions. Certain of these solutions involve the Fourier expansions of the Eisenstei…
Complex dynamics and invariant forms mod p
Alexandru Buium
Complex dynamical systems on the Riemann sphere do not possess ``invariant forms''. However there exist non-trivial examples of dynamical systems, defined over number fields, satis…