Cusp Forms in 𝑆𝟒(Γ𝟎(𝟒𝟕)) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant −𝟒𝟕

Cusp Forms in ๐‘†๐Ÿ’(ฮ“๐ŸŽ(๐Ÿ’๐Ÿ•)) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant โˆ’๐Ÿ’๐Ÿ•

A basis of ๐‘†4(ฮ“0(47)) is given and the formulas for the number of representations of positive integers by some direct sum of the quadratic forms ๐‘ฅ21+๐‘ฅ1๐‘ฅ2+12๐‘ฅ22, 2๐‘ฅ21ยฑ๐‘ฅ1๐‘ฅ2+6๐‘ฅ22, 3๐‘ฅ21ยฑ๐‘ฅ1๐‘ฅ2+4๐‘ฅ22 are determined.

Bibliographic Details
Main Author: BarฤฑลŸ Kendirli
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2012/303492
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spelling doaj-ebcd84ef93474a47948a51a221becd5f2020-11-25T01:56:41ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/303492303492Cusp Forms in ๐‘†๐Ÿ’(ฮ“๐ŸŽ(๐Ÿ’๐Ÿ•)) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant โˆ’๐Ÿ’๐Ÿ•BarฤฑลŸ Kendirli0Department of Mathematics, Faculty of Arts and Sciences, Fatih University, Buyukcekmece, 34500 Istanbul, TurkeyA basis of ๐‘†4(ฮ“0(47)) is given and the formulas for the number of representations of positive integers by some direct sum of the quadratic forms ๐‘ฅ21+๐‘ฅ1๐‘ฅ2+12๐‘ฅ22, 2๐‘ฅ21ยฑ๐‘ฅ1๐‘ฅ2+6๐‘ฅ22, 3๐‘ฅ21ยฑ๐‘ฅ1๐‘ฅ2+4๐‘ฅ22 are determined.http://dx.doi.org/10.1155/2012/303492
collection DOAJ
language English
format Article
sources DOAJ
author BarฤฑลŸ Kendirli
spellingShingle BarฤฑลŸ Kendirli
Cusp Forms in ๐‘†๐Ÿ’(ฮ“๐ŸŽ(๐Ÿ’๐Ÿ•)) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant โˆ’๐Ÿ’๐Ÿ•
International Journal of Mathematics and Mathematical Sciences
author_facet BarฤฑลŸ Kendirli
author_sort BarฤฑลŸ Kendirli
title Cusp Forms in ๐‘†๐Ÿ’(ฮ“๐ŸŽ(๐Ÿ’๐Ÿ•)) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant โˆ’๐Ÿ’๐Ÿ•
title_short Cusp Forms in ๐‘†๐Ÿ’(ฮ“๐ŸŽ(๐Ÿ’๐Ÿ•)) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant โˆ’๐Ÿ’๐Ÿ•
title_full Cusp Forms in ๐‘†๐Ÿ’(ฮ“๐ŸŽ(๐Ÿ’๐Ÿ•)) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant โˆ’๐Ÿ’๐Ÿ•
title_fullStr Cusp Forms in ๐‘†๐Ÿ’(ฮ“๐ŸŽ(๐Ÿ’๐Ÿ•)) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant โˆ’๐Ÿ’๐Ÿ•
title_full_unstemmed Cusp Forms in ๐‘†๐Ÿ’(ฮ“๐ŸŽ(๐Ÿ’๐Ÿ•)) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant โˆ’๐Ÿ’๐Ÿ•
title_sort cusp forms in ๐‘†๐Ÿ’(ฮณ๐ŸŽ(๐Ÿ’๐Ÿ•)) and the number of representations of positive integers by some direct sum of binary quadratic forms with discriminant โˆ’๐Ÿ’๐Ÿ•
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2012-01-01
description A basis of ๐‘†4(ฮ“0(47)) is given and the formulas for the number of representations of positive integers by some direct sum of the quadratic forms ๐‘ฅ21+๐‘ฅ1๐‘ฅ2+12๐‘ฅ22, 2๐‘ฅ21ยฑ๐‘ฅ1๐‘ฅ2+6๐‘ฅ22, 3๐‘ฅ21ยฑ๐‘ฅ1๐‘ฅ2+4๐‘ฅ22 are determined.
url http://dx.doi.org/10.1155/2012/303492
work_keys_str_mv AT barฤฑskendirli cuspformsins4g047andthenumberofrepresentationsofpositiveintegersbysomedirectsumofbinaryquadraticformswithdiscriminant47
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