Modular Relations and Parity in Number Theory
This book describes research problems by unifying and generalizing some remote-looking objects through the functional equation and the parity relation of relevant zeta functions, known as the modular relation or RHB correspondence. It provides examples of zeta functions introduced as absolutely conv...
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Singapore :
Springer Nature Singapore : Imprint: Springer,
2025.
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| Հրատարակություն: | 1st ed. 2025. |
| Շարք: | Infosys Science Foundation Series in Mathematical Sciences,
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| Խորագրեր: | |
| Առցանց հասանելիություն: | https://doi.org/10.1007/978-981-96-6471-9 |
| Ցուցիչներ: |
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| 100 | 1 | |a Chakraborty, Kalyan. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Modular Relations and Parity in Number Theory |h [electronic resource] / |c by Kalyan Chakraborty, Shigeru Kanemitsu, Takako Kuzumaki. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Singapore : |b Springer Nature Singapore : |b Imprint: Springer, |c 2025. | |
| 300 | |a 1 online resource (XII, 267 p. 1 illus.). | ||
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| 505 | 0 | |a Introduction and preliminaries -- Ramified functional equations and (CSIF) -- Unified theory of Epstein zeta-functions & zeta-functions associated with real-analytic automorphic forms -- A unifying principle for modular relations and summation formulas -- Class numbers of Abelian fields and (CPMD) -- Historical remarks. | |
| 520 | |a This book describes research problems by unifying and generalizing some remote-looking objects through the functional equation and the parity relation of relevant zeta functions, known as the modular relation or RHB correspondence. It provides examples of zeta functions introduced as absolutely convergent Dirichlet series, not necessarily with the Euler product. The book generalizes this to broader cases, explaining the special functions involved. The extension of the Chowla–Selberg integral formula and the Hardy transform are key, substituting the Bochner modular relation in the zeta function of Maass forms. The book also develops principles to deduce summation formulas as modular relations and addresses Chowla’s problem and determinant expressions for class numbers. Many books define zeta functions using Euler products, excluding Epstein and Hurwitz-type zeta functions. Euler products are constructed from objects with a unique factorization domain property. This book focuses on using the functional equation, called the modular relation, specifically the ramified functional equation of the Hecker type. Here, the gamma factor is the product of two gamma functions, leading to the Fourier–Whittaker expansion, and reducing to the Fourier–Bessel expansion or the Chowla–Selberg integral formula for Epstein zeta functions. | ||
| 532 | 8 | |a Accessibility summary: This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility. It includes screen reader support, bookmarks for easy navigation, keyboard-friendly links and forms, and searchable, selectable text. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility Please Note that a more accessible version of this eBook is available as an EPUB. | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
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| 588 | |a Print version record. | ||
| 650 | 0 | |a Number theory. | |
| 650 | 1 | 4 | |a Number Theory. |
| 700 | 1 | |a Kanemitsu, Shigeru. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Kuzumaki, Takako. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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