Exact half-BPS black hole entropies in CHL models from Rademacher series oleh Richard Nally

"…Abstract The microscopic spectrum of half-BPS excitations in toroidally compactified heterotic string theory has been computed exactly through the use of results from analytic number theory. Recently, similar quantities have been understood macroscopically by evaluating the gravitational path integral on the M-theory lift of the AdS2 near-horizon geometry of the corresponding black hole. …"
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Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits oleh Cameron Calcluth, Alessandro Ferraro, Giulia Ferrini

"…This method involves evaluating a transformed Jacobi theta function using techniques from analytic number theory. We then use this result to identify two large classes of multimode circuits which are classically efficiently simulatable and are not contained by the GKP encoded Clifford group. …"
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Some Results on Multifractal Spectral Analysis oleh Roberto N. Padua, Efren O. Barabat, Mark S. Borres, Randy K. Salazar

"…The study ends by providing possible avenues for future research particularly in the area of analytic number theory in relation to the Riemann hypothesis about the distribution of primes.…"
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Some identities on generalized harmonic numbers and generalized harmonic functions oleh Kim Dae San, Kim Hyekyung, Kim Taekyun

"…The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory, and analysis of algorithms. The aim of this article is to derive some identities involving generalized harmonic numbers and generalized harmonic functions from the beta functions Fn(x)=B(x+1,n+1),(n=0,1,2,…){F}_{n}\left(x)=B\left(x+1,n+1),\left(n=0,1,2,\ldots ) using elementary methods. …"
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Symmetries and spectral statistics in chaotic conformal field theories. Part II. Maass cusp forms and arithmetic chaos oleh Felix M. Haehl, Wyatt Reeves, Moshe Rozali

"…Both their eigenvalues and Fourier coefficients are sporadic discrete numbers with interesting statistical properties and relations to analytic number theory; this is referred to as ‘arithmetic chaos’. …"
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Understanding Harmonic Structures Through Instantaneous Frequency oleh Marco S. Fabus, Mark W. Woolrich, Catherine W. Warnaby, Andrew J. Quinn

"…We explore the mathematics of our definition and link it to results from analytic number theory. This naturally leads to us to define two classes of harmonic structures, termed strong and weak, with different extrema behaviour. …"
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The positive integral points on the elliptic curve 𝒚𝟐=𝟕𝒑𝒙(𝒙𝟐+𝟖) oleh Xiancun Du, Zhao Jianhong, Yang Lixing

"…The integral point of elliptic curve is a very important problem in both elementary number theory and analytic number theory. In recent years, scholars have paid great attention to solving the problem of positive integer points on elliptic curve 𝑦2 = 𝑘(𝑎𝑥2+𝑏𝑥+𝑐), where 𝑘,𝑎,𝑏,𝑐 are integers. …"
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On 2-variable q-Hermite polynomials oleh Nusrat Raza, Mohammed Fadel, Kottakkaran Sooppy Nisar, M. Zakarya

"…It has wide applications, particularly in quantum mechanics, analytic number theory, combinatorial analysis, operation theory etc. …"
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Exponential sums with reducible polynomials oleh Cécile Dartyge, Greg Martin

"…The concept of equidistribution is a central one in analytic number theory, and also in the subfield of combinatorics known as discrepancy theory. …"
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Multivariate polynomial values in difference sets oleh John R. Doyle, Alex Rice

"…Szemerédi's original proof of Szemerédi's theorem was purely combinatorial, but soon after it was discovered, Furstenberg pioneered an approach via ergodic theory, which also yielded (more simply) the result about square differences, which was proved independently by Sárközy using methods from analytic number theory. These different approaches naturally led to research programmes with slightly different emphases: ergodic theorists pursued qualitative generalizations, a particular highlight of which is the Bergelson-Leibman theorem, a "polynomial Szemerédi theorem" that simultaneously generalizes the two theorems just mentioned, while additive combinatorialists and analytic number theorists pursued more quantitative aspects, aiming to understand how dense a subset of $\{1,2,\dots,n\}$ has to be in order to guarantee that it contains a substructure of a given kind. …"
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Ergodicity of the Liouville system implies the Chowla conjecture oleh Nikos Frantzikinakis

"…Several powerful tools from analytic number theory, additive combinatorics, and ergodic theory are used in the proof. …"
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Fast Calculation of Bernoulli Numbers oleh Rustem R. Aidagulov, Sergei T. Glavatsky

"…Bernoulli numbers are often found in mathematical analysis, number theory, combinatorics, and other areas of mathematics. …"
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Influence of the number system in residual classes on the fault tolerance of the computer system oleh Alina Yanko, Viktor Krasnobayev, Anatolii Martynenko

"…Methods of system analysis, number theory, theory of computing processes and systems, and coding theory in the SRC were the basis of the conducted research. …"
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The Bombieri-Vinogradov theorem for nilsequences oleh Xuancheng Shao, Joni Teräväinen

"…The Bombieri-Vinogradov theorem is a major result in analytic number theory that shows that on average the error term is of the kind of size that the generalized Riemann hypothesis predicts. …"
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Discrepancy of High-Dimensional Permutations oleh Nathan Linial, Zur Luria

"…An important branch of combinatorics, with links to analysis, number theory and other areas, is discrepancy theory. …"
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Estimate of the module of analogue Weyls trigonometrical sum in ring of Gaussian numbers oleh Pavel Nikolaevich Sorokin

"…The estimation of the module of some analogue of Weyl's trigonometrical sum with summation on Gaussian numbers is proved by methods of the analytical number theory. Multiplicative norm of Gaussian numbers is less than some integer.…"
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Linear programming over exponent pairs oleh Lelechenko Andrew V.

"…The output of the algorithm leads to the improvement and establishing new estimates in the various divisor problems in the analytical number theory.…"
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