Motivic Poisson Summation
نویسندگان
چکیده
منابع مشابه
Motivic Poisson Summation
We develop a “motivic integration” version of the Poisson summation formula for function fields, with values in the Grothendieck ring of definable exponential sums. We also study division algebras over the function field, and show (under some assumptions) that the Fourier transform of a conjugation-invariant test function does not depend on the form of the division algebra. This yields a motivi...
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Abstract. Euler–Maclaurin and Poisson analogues of the summations ∑a<n≤b χ(n) f (n), ∑a<n≤b d(n) f (n), ∑a<n≤b d(n)χ(n) f (n) have been obtained in a unified manner, where (χ(n)) is a periodic complex sequence; d(n) is the divisor function and f (x) is a sufficiently smooth function on [a,b]. We also state a generalised Abel’s summation formula, generalised Euler’s summation formula and Euler’s...
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ژورنال
عنوان ژورنال: Moscow Mathematical Journal
سال: 2009
ISSN: 1609-3321,1609-4514
DOI: 10.17323/1609-4514-2009-9-3-569-623