Discrepancies of products of zeta-regularized products
نویسندگان
چکیده
منابع مشابه
Zeta regularization of infinite products
The problem of regularizing infinite products is a long standing one in mathematical and theoretical physics, as well as in mathematics, of course. Several either formal or rigorous techniques have been introduced. One that obtained an undiscussed favor is the zeta regularization. The idea is simple to write down in a formal way (so as it as been used for a long times by physicists), and has go...
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The numerator over c is the Ramanujan sum ∑ (a,c)=1 cos( 2πma c ). This identity clearly displays the oscillations of σ(m) around its mean value π m 6 . Also, (1.1) makes sense as a limit when m = 0 and gives the extension σ(0) = − 1 24 . There is a nice generalization of Ramanujan’s formula, that goes back to Petersson and Rademacher, that connects it with the theory of modular forms (see Knop...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2012
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2012.v19.n1.a16