On the arithmetic nature of coefficients of multiplicative eta-functions
In the article we study the arithmetic nature of the coefficients of multiplicative eta-products, also called McKay functions. For some functions it is possible to establish Hecke correspondence between the coefficients of McKay and Hecke grossen-characters of imaginary quadratic fields. For other M...
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Samara National Research University
2025-06-01
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| Series: | Вестник Самарского университета: Естественнонаучная серия |
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| Online Access: | https://journals.ssau.ru/est/article/viewFile/28668/11308 |
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| author | G. V. Voskresenskaya |
| author_facet | G. V. Voskresenskaya |
| author_sort | G. V. Voskresenskaya |
| collection | DOAJ |
| description | In the article we study the arithmetic nature of the coefficients of multiplicative eta-products, also called McKay functions. For some functions it is possible to establish Hecke correspondence between the coefficients of McKay and Hecke grossen-characters of imaginary quadratic fields. For other McKay functions such a correspondence is impossible but their coefficients can be represented as sums containing Hecke characters. The emerging Hecke characters are written out explicitly. In the article we write the first ten coefficients for all McKay functions. Calculations are based on Euler’s pentagonal formula. The article also talks about the connection between the coefficients of these functions and Shimura sums. |
| format | Article |
| id | doaj-art-923df1f54d9a47eca59804d48d9aedeb |
| institution | Kabale University |
| issn | 2541-7525 2712-8954 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Вестник Самарского университета: Естественнонаучная серия |
| spelling | doaj-art-923df1f54d9a47eca59804d48d9aedeb2025-08-20T03:31:20ZengSamara National Research UniversityВестник Самарского университета: Естественнонаучная серия2541-75252712-89542025-06-0131172110.18287/2541-7525-2025-31-1-7-218838On the arithmetic nature of coefficients of multiplicative eta-functionsG. V. Voskresenskaya0https://orcid.org/0000-0002-6288-5372Samara National Research UniversityIn the article we study the arithmetic nature of the coefficients of multiplicative eta-products, also called McKay functions. For some functions it is possible to establish Hecke correspondence between the coefficients of McKay and Hecke grossen-characters of imaginary quadratic fields. For other McKay functions such a correspondence is impossible but their coefficients can be represented as sums containing Hecke characters. The emerging Hecke characters are written out explicitly. In the article we write the first ten coefficients for all McKay functions. Calculations are based on Euler’s pentagonal formula. The article also talks about the connection between the coefficients of these functions and Shimura sums.https://journals.ssau.ru/est/article/viewFile/28668/11308modular formscusp formsfourier coefficientsquadratic fieldshecke charactersq-seriesmultiplicative functionseuler’s pentagonal formulashimura sums. |
| spellingShingle | G. V. Voskresenskaya On the arithmetic nature of coefficients of multiplicative eta-functions Вестник Самарского университета: Естественнонаучная серия modular forms cusp forms fourier coefficients quadratic fields hecke characters q-series multiplicative functions euler’s pentagonal formula shimura sums. |
| title | On the arithmetic nature of coefficients of multiplicative eta-functions |
| title_full | On the arithmetic nature of coefficients of multiplicative eta-functions |
| title_fullStr | On the arithmetic nature of coefficients of multiplicative eta-functions |
| title_full_unstemmed | On the arithmetic nature of coefficients of multiplicative eta-functions |
| title_short | On the arithmetic nature of coefficients of multiplicative eta-functions |
| title_sort | on the arithmetic nature of coefficients of multiplicative eta functions |
| topic | modular forms cusp forms fourier coefficients quadratic fields hecke characters q-series multiplicative functions euler’s pentagonal formula shimura sums. |
| url | https://journals.ssau.ru/est/article/viewFile/28668/11308 |
| work_keys_str_mv | AT gvvoskresenskaya onthearithmeticnatureofcoefficientsofmultiplicativeetafunctions |