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We present a remarkably simple and surprisingly natural interpretation of thevalues of zeta functions at negative integers and zero. Namely we are able torelate these values to areas related to partial sums of powers. We apply theseresults to further interpretations of values of $L$-functions at negativeintegers. We hint in a very brief way at some expected connections of this workwith other current efforts to understand the mysteries of the values of zetafunctions at integers.

Further insights into the mysteries of the values of zeta functions at integers