TY - JOUR

T1 - On the norm of Krasner analytic functions with applications to transcendence results

AU - Alexandru, V.

AU - Niţu, C. C.

AU - Vâjâitu, M.

AU - Zaharescu, Alexandru

PY - 2015/10/1

Y1 - 2015/10/1

N2 - Given a prime number p let Cp be the Tate field i.e. the topological completion of the algebraic closure of the field of p-adic numbers with respect to the p-adic absolute value. We give an estimate of the norm of Krasner analytic functions defined on the complement of a fundamental set X of Cp, which are Cauchy transforms obtained by integrating against strongly Lipschitz distributions on X. The functions from a specific class of the above representations are transcendental over Cp(Z) and, as a consequence, we obtain transcendence results related to the twisted p-adic log gamma function and the trace functions. The twisted p-adic log gamma function and its derivatives are linearly independent over Cp(Z) and, moreover, all their zeros are algebraic.

AB - Given a prime number p let Cp be the Tate field i.e. the topological completion of the algebraic closure of the field of p-adic numbers with respect to the p-adic absolute value. We give an estimate of the norm of Krasner analytic functions defined on the complement of a fundamental set X of Cp, which are Cauchy transforms obtained by integrating against strongly Lipschitz distributions on X. The functions from a specific class of the above representations are transcendental over Cp(Z) and, as a consequence, we obtain transcendence results related to the twisted p-adic log gamma function and the trace functions. The twisted p-adic log gamma function and its derivatives are linearly independent over Cp(Z) and, moreover, all their zeros are algebraic.

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U2 - 10.1016/j.jpaa.2015.02.033

DO - 10.1016/j.jpaa.2015.02.033

M3 - Article

AN - SCOPUS:84929519065

VL - 219

SP - 4607

EP - 4618

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 10

ER -