Elliptic Curves, Modular Forms, L-Functions and Applications

Dear Colleagues,

This Special Issue of Axioms focuses on the intricate and profound connections between elliptic curves, modular forms, their associated L-functions, and related topics. These areas represent the fundamental pillars of modern number theory, with far-reaching implications in pure and applied mathematics, such as combinatorics, cryptography, coding theory, mathematical physics, etc.

The scope of this Special Issue encompasses theoretical advancements, computational breakthroughs, and the interdisciplinary applications of these topics. Areas of interest include, but are not limit to, the arithmetic of elliptic curves, modular forms and their generalizations, analytic and algebraic properties of L-functions, and applications in number theory and combinatorics.

The purpose of this Special Issue is to provide a platform for the dissemination of cutting-edge research that deepens our understanding of elliptic curves, modular forms, and L-functions while fostering dialogue among researchers across different mathematical disciplines. By bringing together a diverse collection of original research papers and surveys, this Special Issue aims to achieve the following:

1. Highlight recent developments in the theory of elliptic curves, including, but not limit to, the Birch and Swinnerton-Dyer conjecture, the rank of elliptic curves, and their rational points.
2. Explore the role of modular forms and their generalizations in arithmetic geometry, number theory, and combinatorics.
3. Examine the analytic and arithmetic properties of L-functions, particularly their connections to special values, algebraic cycles, etc.
4. Showcase innovative computational approaches and algorithms that enhance the understanding and application of these mathematical structures.
5. Encourage interdisciplinary research by highlighting the applications of elliptic curves, modular forms, and L-functions in cryptography, coding theory, and other areas.

Dr. Dongxi Ye
Prof. Dr. Fabio Caldarola
Guest Editors

Manuscript Submission Information

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