ayoub teymornejad by ayoub teymornejad
Abstract
The Riemann zeta function is one of the most enigmatic constructs in mathematics, oft... more Abstract
The Riemann zeta function is one of the most enigmatic constructs in mathematics, often associated with the distribution of prime numbers. In this study, we argue that the trivial zeros of the zeta function, occurring at negative integers, have no direct connection to real primes. Negative numbers, as abstract complements of natural numbers, serve as analytical tools rather than tangible entities. By examining the functional equation of ζ(s) and the nature of its trivial zeros, we demonstrate that their existence is entirely a product of analytical structure, independent of prime numbers. This perspective challenges conventional interpretations and emphasizes the zeta function as an independent mathematical entity, bridging objective and abstract realms, and inviting a more realistic and profound understanding of mathematics beyond intuition or emotional reasoning.
Abstract
This paper by Ayoub Teymornejad (ایوب تیمورنژاد) presents a novel matrix framework un... more Abstract
This paper by Ayoub Teymornejad (ایوب تیمورنژاد) presents a novel matrix framework unifying integration and differentiation through a determinant-based operator. The approach reveals deep structural links between integrals, derivatives, and function classes. Functions such as exponentials and trigonometric types yield zero determinants, while power, logarithmic, and tangent functions produce nonzero determinants. Proven theorems establish conditions for determinant vanishing, supported by analytic proofs and numerical simulations. This unified matrix-determinant method provides new tools for solving differential equations, validating numerical methods, and modeling dynamical systems, offering a fresh paradigm in mathematical analysis.
Abstract
This paper by Ayoub Teymornejad (ایوب تیمورنژاد) presents the discovery and analysis ... more Abstract
This paper by Ayoub Teymornejad (ایوب تیمورنژاد) presents the discovery and analysis of symmetric exponential functions and operators defined specifically for prime numbers. By replacing general variables with primes, a new mathematical framework emerges, introducing indivisibility theorems, asymmetry measures, and determinant-based properties unique to primes. Novel analytical formulas, Ramanujan-type series, and distribution functions are proposed, uncovering deep exponential structures hidden in prime numbers. Numerical computations illustrate the behavior of these functions, revealing patterns with strong implications for number theory. Beyond pure mathematics, the results demonstrate significant potential applications in post-quantum cryptography, where prime-based exponential operators can strengthen encryption, and in theoretical physics, particularly in modeling dynamical systems and quantum energy structures. This study not only provides new insights into the nature of primes but also opens innovative avenues for advancing number theory, cryptographic algorithms, and interdisciplinary applications in modern physics.
چکیده
این مقاله، تألیف ایوب تیمورنژاد (Ayoub Teymornejad)، به کشف و تحلیل توابع نمایی متقارن و... more چکیده
این مقاله، تألیف ایوب تیمورنژاد (Ayoub Teymornejad)، به کشف و تحلیل توابع نمایی متقارن و عملگرهای اعداد اول می‌پردازد، به‌طوری که اعداد اول جایگزین متغیرهای عمومی شده‌اند. با تعمیم روابط کلاسیک به اعداد اول، قضایای نوین، روابط عدم بخش‌پذیری و معیارهای نامتقارن معرفی می‌شوند. فرمول‌ها و سری‌های تحلیلی جدید رفتار نمایی اعداد اول را آشکار کرده و ابزارهای قدرتمندی برای بررسی الگوهای بنیادین آن‌ها ارائه می‌دهند. این پژوهش کاربردهایی در رمزنگاری پساکوانتومی، تحلیل سیستم‌های دینامیکی در فیزیک نظری و توسعه الگوریتم‌های پیشرفته در نظریه اعداد دارد. نتایج نشان می‌دهند که توابع نمایی متقارن اعداد اول می‌توانند خواص و الگوهای پنهان آن‌ها را آشکار کنند و مسیرهای جدیدی برای تحقیقات آینده در ریاضیات خالص و کاربردی باز کنند.
Abstract
Environmental Gravity Theory, proposed by Ayoub Teymornejad (ایوب تیمورنژاد), present... more Abstract
Environmental Gravity Theory, proposed by Ayoub Teymornejad (ایوب تیمورنژاد), presents a groundbreaking framework where gravity depends on environmental conditions such as velocity, density, and temperature. This theory offers a unified description of gravitational interactions across cosmic, planetary, and atomic scales, explaining phenomena like dark matter, dark energy, and subtle variations in atomic spectra. By integrating environmental functions directly into field equations, it provides testable predictions and opens new avenues for experimental physics, space exploration, and advanced technologies.
Uploads
ayoub teymornejad by ayoub teymornejad
The Riemann zeta function is one of the most enigmatic constructs in mathematics, often associated with the distribution of prime numbers. In this study, we argue that the trivial zeros of the zeta function, occurring at negative integers, have no direct connection to real primes. Negative numbers, as abstract complements of natural numbers, serve as analytical tools rather than tangible entities. By examining the functional equation of ζ(s) and the nature of its trivial zeros, we demonstrate that their existence is entirely a product of analytical structure, independent of prime numbers. This perspective challenges conventional interpretations and emphasizes the zeta function as an independent mathematical entity, bridging objective and abstract realms, and inviting a more realistic and profound understanding of mathematics beyond intuition or emotional reasoning.
This paper by Ayoub Teymornejad (ایوب تیمورنژاد) presents a novel matrix framework unifying integration and differentiation through a determinant-based operator. The approach reveals deep structural links between integrals, derivatives, and function classes. Functions such as exponentials and trigonometric types yield zero determinants, while power, logarithmic, and tangent functions produce nonzero determinants. Proven theorems establish conditions for determinant vanishing, supported by analytic proofs and numerical simulations. This unified matrix-determinant method provides new tools for solving differential equations, validating numerical methods, and modeling dynamical systems, offering a fresh paradigm in mathematical analysis.
This paper by Ayoub Teymornejad (ایوب تیمورنژاد) presents the discovery and analysis of symmetric exponential functions and operators defined specifically for prime numbers. By replacing general variables with primes, a new mathematical framework emerges, introducing indivisibility theorems, asymmetry measures, and determinant-based properties unique to primes. Novel analytical formulas, Ramanujan-type series, and distribution functions are proposed, uncovering deep exponential structures hidden in prime numbers. Numerical computations illustrate the behavior of these functions, revealing patterns with strong implications for number theory. Beyond pure mathematics, the results demonstrate significant potential applications in post-quantum cryptography, where prime-based exponential operators can strengthen encryption, and in theoretical physics, particularly in modeling dynamical systems and quantum energy structures. This study not only provides new insights into the nature of primes but also opens innovative avenues for advancing number theory, cryptographic algorithms, and interdisciplinary applications in modern physics.
این مقاله، تألیف ایوب تیمورنژاد (Ayoub Teymornejad)، به کشف و تحلیل توابع نمایی متقارن و عملگرهای اعداد اول می‌پردازد، به‌طوری که اعداد اول جایگزین متغیرهای عمومی شده‌اند. با تعمیم روابط کلاسیک به اعداد اول، قضایای نوین، روابط عدم بخش‌پذیری و معیارهای نامتقارن معرفی می‌شوند. فرمول‌ها و سری‌های تحلیلی جدید رفتار نمایی اعداد اول را آشکار کرده و ابزارهای قدرتمندی برای بررسی الگوهای بنیادین آن‌ها ارائه می‌دهند. این پژوهش کاربردهایی در رمزنگاری پساکوانتومی، تحلیل سیستم‌های دینامیکی در فیزیک نظری و توسعه الگوریتم‌های پیشرفته در نظریه اعداد دارد. نتایج نشان می‌دهند که توابع نمایی متقارن اعداد اول می‌توانند خواص و الگوهای پنهان آن‌ها را آشکار کنند و مسیرهای جدیدی برای تحقیقات آینده در ریاضیات خالص و کاربردی باز کنند.
Environmental Gravity Theory, proposed by Ayoub Teymornejad (ایوب تیمورنژاد), presents a groundbreaking framework where gravity depends on environmental conditions such as velocity, density, and temperature. This theory offers a unified description of gravitational interactions across cosmic, planetary, and atomic scales, explaining phenomena like dark matter, dark energy, and subtle variations in atomic spectra. By integrating environmental functions directly into field equations, it provides testable predictions and opens new avenues for experimental physics, space exploration, and advanced technologies.