Titlebook: Introduction to Applications of Modular Forms; Computational Aspect Zafer Selcuk Aygin Book 2023 The Editor(s) (if applicable) and The Auth

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Introduction to Applications of Modular Forms978-3-031-32629-5Series ISSN 1938-1743 Series E-ISSN 1938-1751

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https://doi.org/10.1007/978-3-031-32629-5Modular Forms; q-series; Eisenstein Series; Dedekind eta Function; Partitions; Quadratic Forms; Siegel’s F

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Dirichlet Characters,In this chapter we introduce the preliminary tools. These include Dirichlet characters, Gauss sums, Dirichlet .-functions and Bernoulli numbers.

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Book 2023theory of modular forms and its applications in number theoretic problems such as representations by quadratic forms and the determination of asymptotic formulas for Fourier coefficients of different types of special functions. A detailed account of recent applications of modular forms in number the

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Book 2023ic formulas for Fourier coefficients of different types of special functions. A detailed account of recent applications of modular forms in number theory with a focus on using computer algorithms is provided. Computer algorithms are included for each presented application to help readers put the theory in context and make new conjectures.??.

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Various Applications,oduce the idea of using eta quotients together with the character analog of Dedekind’s eta function to produce cusp forms. In the final section, we use the Modularity Theorem to give an application of modular forms on elliptic curves.

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dbreaking branch of contemporary ethics because of its environmentally embedded and embodied conception of human beings. For a change towards a more sustainable culture to take place it is however not enough that our understanding of our place in the environment becomes more ecocentric and to realiz