Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Kronecker formula for Bernoulli numbers and
  self-intersections of curves on a surface   We present a new explicit formula for the $m$-th Bernoulli number $B_m$,
which involves two integer parameters $a$ and $n$ with $0\le a\le m\le n$. If
we set $a=0$ and $n=m$, then the formula reduces to the celebrated Kronecker
formula for $B_m$. We give two proofs of our formula. One is analytic and uses
a certain function in two variables. The other is algebraic and is motivated by
a topological consideration of self-intersections of curves on an oriented
surface.

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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph