Systolic convolution of arithmetic functions
نویسندگان
چکیده
منابع مشابه
The Convolution Ring of Arithmetic Functions and Symmetric Polynomials
Inspired by Rearick (1968), we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving generalized Lucas polynomials. The EXP is the inverse of LOG. In particular, LOG takes a convolution product of generalized Fibonacci polynomials to a sum of generalized Lucas polynomials and EXP takes the sum to the convolution product. We use this structure to ...
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Arithmetic convolution rings provide a general and unified treatment of many rings that have been called arithmetic; the best known examples are rings of complex valued functions with domain in the set of non-negative integers and multiplication the Cauchy product or the Dirichlet product. The emphasis here is on factorization and related properties of such rings which necessitates prior result...
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The Cauchy-type product of two arithmetic functions f and g on nonnegative integers is defined by (f • g)(k) := ∑k m=0 ( k m ) f(m)g(k −m). We explore some algebraic properties of the aforementioned convolution, which is a fundamental characteristic of the identities involving the Bernoulli numbers, the Bernoulli polynomials, the power sums, the sums of products, and so forth.
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In the beginning of 1998 Gerard van de Geer and René Schoof posted a beautiful preprint (cf. [2]). Among other things in this preprint they defined exactly h(L) for Arakelov line bundles L on an “arithmetic curve”, i.e. a number field. The main advantage of their definition was that they got an exact analog of the Riemann-Roch formula h(L) − h0(K−L) = degL+1−g. Before that h(L) was defined as a...
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In the beginning of 1998 Gerard van der Geer and Ren e Schoof posted a beautiful preprint (cf. [2]). Among other things in this preprint they de ned exactly h(L) for Arakelov line bundles L on an \arithmetic curve", i.e. a number eld. The main advantage of their de nition was that they got an exact analog of the Riemann-Roch formula h(L) h(K L) = degL+1 g: Before that h(L) was de ned as an inte...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1992
ISSN: 0304-3975
DOI: 10.1016/0304-3975(92)90265-h