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Keywords:
$p$-adic integral; $p$-adic measures; Bernoulli numbers; Genocchi numbers; Genocchi polynomials; tangent coefficients; Kummer congruences
$p$-adic integral; $p$-adic measures; Bernoulli numbers; Genocchi numbers; Genocchi polynomials; tangent coefficients; Kummer congruences
Summary:
We use the properties of $p$-adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.
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