Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
The convolution sum, [...] ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms are used to achieve these evaluations. Since the modular space of level 22 is contained in that of level 44, we almost completely use the basis elements of the modular space of level 44 to carry out the evaluation of the convolution sums for αβ = 22. We then use these convolution sums to determine formulae for the number of representations of a positive integer by the octonary quadratic forms [...] a(x12+x22+x32+x42)+b(x52+x62+x72+x82), $a\,(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2})+b\,(x_{5}^{2}+x_{6}^{2}+x_{7}^{2}+x_{8}^{2}),$ where (a, b) = (1, 11), (1, 13).
Kategorie tematyczne
- 11A25: Arithmetic functions; related numbers; inversion formulas
- 11E20: General ternary and quaternary quadratic forms; forms of more than two variables
- 11F27: Theta series; Weil representation; theta correspondences
- 11F20: Dedekind eta function, Dedekind sums
- 11F11: Holomorphic modular forms of integral weight
- 11E25: Sums of squares and representations by other particular quadratic forms
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
446-458
Opis fizyczny
Daty
wydano
2017-01-01
otrzymano
2016-08-30
zaakceptowano
2017-02-28
online
2017-04-18
Twórcy
autor
- Centre for Research in Algebra and Number Theory, School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6,
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2017-0041