相关论文: Ramanujan's influence on string theory, black hole…
Explorations of quantum black holes in string theory have led to fascinating connections with the work of Ramanujan on partitions and mock theta functions, which in turn relate to diverse topics in number theory and enumerative geometry.…
The study of black holes in string theory has led to the discovery of deep and surprising connections between black holes and modular forms -- which are two classical, a priori unrelated, subjects. This article explains the main physical…
The word moonshine refers to unexpected relations between the two distinct mathematical structures: finite group representations and modular objects. It is believed that the key to understanding moonshine is through physical theories with…
We briefly review some of Ramanujan's contributions to mathematics, including his $1/\pi$ series, his work on modular forms, and his work on partitions. We briefly review his life, including his collaboration with Hardy. Finally, we give a…
Mock modular forms, first invented by Ramanujan, provide a beautiful generalization of the usual modular forms. In recent years, it was found that they capture generating functions of the number of microstates of BPS black holes appearing…
A number theoretical model of $1/f$ noise found in phase locked loops is developed. The dynamics of phases and frequencies involved in the nonlinear mixing of oscillators and the low-pass filtering is formulated thanks to the rules of the…
The perturbations of string-theoretic black holes are analyzed by generalizing the method of Chandrasekhar. Attention is focussed on the case of the recently considered charged string-theoretic black hole solutions as a representative…
Ramanujan's Master Theorem is a decades-old theorem in the theory of Mellin transforms which has wide applications in both mathematics and high energy physics. The unconventional method of Ramanujan in his proof of the theorem left…
Eisenstein series play an important role in the theory of modular forms and have profound connections with $q$-series identities, partition theory, and special functions. Likewise, Ramanujan's mock theta functions, originally introduced in…
Mock modular forms have found applications in numerous branches of mathematical sciences since they were first introduced by Ramanujan nearly a century ago. In this proceeding we highlight a new area where mock modular forms start to play…
Throughout his entire mathematical life, Ramanujan loved to evaluate definite integrals. One can find them in his problems submitted to the \emph{Journal of the Indian Mathematical Society}, notebooks, Quarterly Reports to the University of…
Monstrous moonshine relates distinguished modular functions to the representation theory of the monster. The celebrated observations that 196884=1+196883 and 21493760=1+196883+21296876, etc., illustrate the case of the modular function…
We give an elementary review of black holes in string theory. We discuss black hole entropy from string microstates and Hawking radiation from these states. We then review the structure of 2-charge microstates, and explore how…
The study of Ramanujan-type congruences for functions specific to additive number theory has a long and rich history. Motivated by recent connections between divisor sums and overpartitions via congruences in arithmetic progressions, we…
We survey divisibility properties of the Fourier coefficients of modular functions inspired by Ramanujan. Then using recent results of the generalized Hecke operator on harmonic Maass functions and known divisibility of Fourier coefficients…
The study of Fourier coefficients of meromorphic modular forms dates back to Ramanujan, who, together with Hardy, studied the reciprocal of the weight 6 Eisenstein series. Ramanujan conjectured a number of further identities for other…
Ramanujan studied the analytic properties of many $q$-hypergeometric series. Of those, mock theta functions have been particularly intriguing, and by work of Zwegers, we now know how these curious $q$-series fit into the theory of…
We review recent progress in our understanding of the physics of black holes. In particular, we discuss the ideas from string theory that explain the entropy of black holes from a counting of microstates of the hole, and the related…
This work explores the shadow of a black hole within the framework of $F(R)$-ModMax gravity coupled with a cloud of strings. The Einstein field equations are solved for a nonlinear ModMax electromagnetic source in the context of $F(R)$…
Perturbations of black holes, initially considered in the context of possible observations of astrophysical effects, have been studied for the past ten years in string theory, brane-world models and quantum gravity. Through the famous…