Atlas: Bernoulli numbers and polynomials via residues by I-Chiau Huang

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Turku Symposium on Number Theory in Memory of Kustaa Inkeri
May 31 - June 4, 1999
University of Turku
Turku, Finland

Organizers
Matti Jutila, Tauno Metsänkylä

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Bernoulli numbers and polynomials via residues
by
I-Chiau Huang
Academia Sinica
Coauthors: Su-Yun Huang

This talk is about identities involving Bernoulli numbers and polynomials, which will appear in J. of Number Theory. Using local cohomology residues, we discover complete sum theorems for Bernoulli numbers and polynomials. Various identities, for instance

n-1
å
k=1
\binom2n2k4^2k6^2n-2kB_2kB_2n-2k = (2²ⁿ-4²ⁿ-6²ⁿ-2²ⁿ⁺¹n)B_2n+(16n)6^2n-2B_2n-1( 1
3
),

arise naturally from here. The complete sum theorems not only provide straightforward verification of known identities but also give new viewpoints towards structure of Bernoulli numbers and polynomials.

Date received: March 30, 1999