Special Issue: “q-Series and Related Topics in Special Functions and Analytic Number Theory”—Foreword by Hari M. Srivastava

“…The following Special Issue: “q-Series and Related Topics in Special Functions and Analytic Number Theory” (see [1–8] below) is an outcome of the ongoing importance and popularity of such topics as Basic (or q-) Series and Basic (or q-) Polynomials.…”
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A Survey of Some Recent Developments on Higher Transcendental Functions of Analytic Number Theory and Applied Mathematics by Hari Mohan Srivastava

“…Often referred to as special functions or mathematical functions, the origin of many members of the remarkably vast family of higher transcendental functions can be traced back to such widespread areas as (for example) mathematical physics, analytic number theory and applied mathematical sciences. …”
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Counting Functions to Generate The Primes in the RSA Algorithm and Diffie-Hellman Key Exchange by Faez Ali AL-Maamori, Mazin Saied Rashid

Subjects: “…(RSA algorithm and Diffie-Hellman exchange, Beurling Primes, Analytic number theory).…”
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Li's criterion for the Riemann hypothesis - numerical approach by Krzysztof Maślanka

Subjects: “…numerical methods in analytic number theory…”
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Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications by Asifa Tassaddiq

Subjects: “…analytic number theory…”
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A New Representation for Srivastava’s λ-Generalized Hurwitz-Lerch Zeta Functions by Asifa Tassaddiq

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Differential Subordination Results for Certain Integrodifferential Operator and Its Applications by M. A. Kutbi, A. A. Attiya

“…Applications in Analytic Number Theory are also obtained which give new results for Hurwitz-Lerch Zeta function and Polylogarithmic function.…”
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Evaluating one-loop string amplitudes by Lorenz Eberhardt, Sebastian Mizera

“…Our method involves a deformation of the integration contour over the modular parameter $\tau$ to a fractal contour introduced by Rademacher in the context of analytic number theory. This procedure leads to explicit and practical formulas for the one-loop four-point amplitudes in type-I superstring theory, amenable to numerical evaluation. …”
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Algebraic, Analytic, and Computational Number Theory and Its Applications by Diana Savin, Nicusor Minculete, Vincenzo Acciaro

“…Analytic number theory is a branch of number theory which inherits methods from mathematical analysis in order to solve difficult problems about the integers [...]…”
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The Distribution Properties of Consecutive Quadratic Residue Sequences by Xiao Wang, Hao Fang

“…In this paper, we apply analytic number theory methods, in particular, properties of Legendre’s symbol modulo p and character sums, to study the numbers Npk,s and Np′k,s. …”
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Asymptotic behaviour of a non-commutative rational series with a nonnegative linear representation by Philippe Dumas, Helger Lipmaa, Johan Wallén

“…We analyse the asymptotic behaviour in the mean of a non-commutative rational series, which originates from differential cryptanalysis, using tools from probability theory, and from analytic number theory. We derive a Fourier representation of a first-order summation function obtained by interpreting this rational series as a non-classical rational sequence via the octal numeration system. …”
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Generalized polynomial exponential sums and their fourth power mean by Li Wang, Yuanyuan Meng

“…The study of the power mean of the generalized polynomial exponential sums plays a very important role in analytic number theory, and many classical number theory problems are closely related to it. …”
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On two-term exponential sums and their mean values by Jianghua Li, Zepeng Zhang, Tianyu Pan

“…The mean value problems of exponential sums play a very important role in the research of analytic number theory, and many famous number theory problems are closely related to them. …”
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Some identities related to Riemann zeta-function by Lin Xin

“…Abstract It is well known that the Riemann zeta-function ζ ( s ) $\zeta(s)$ plays a very important role in the study of analytic number theory. In this paper, we use the elementary method and some new inequalities to study the computational problem of one kind of reciprocal sums related to the Riemann zeta-function at the integer point s ≥ 2 $s\geq2$ , and for the special values s = 2 , 3 $s=2, 3$ , we give two exact identities for the integer part of the reciprocal sums of the Riemann zeta-function. …”
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On the General Divergent Arithmetic Sums over the Primes and the Symmetries of Riemann’s Zeta Function by Luis Acedo

“…In classical analytic number theory, the sum of the logarithm of the prime numbers plays a crucial role. …”
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On the conformal spin dependence of the perturbative QCD vacuum singularity by Grigorios Chachamis, Agustín Sabio Vera

“…An alternative formulation is possible when connecting this Fourier expansion with Bessel kernels studied in analytic number theory.…”
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Mertens’ Theorem for some certain intermediate growths by Sawian Jaidee

“…The way of finding such asymptotic expressions is an analogue of Mertens’ Theorem in analytic number theory. In this article, we focus on the dynamical Mertens' Theorem of some certain growths in case S and its complement are infinite subsets of all rational primes. …”
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Lerch-harmonic numbers related to Lerch transcendent by Taekyun Kim, Dae San Kim, Jongkyum Kwon, Hyunseok Lee

“…ABSTRACTHarmonic numbers and generalized harmonic numbers have been studied in connection with combinatorial problems, many expressions involving special functions in analytic number theory and analysis of algorithms. We introduce Lerch-harmonic numbers which generalize the harmonic numbers and the generalized harmonic numbers. …”
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Generating safe primes by von zur Gathen Joachim, Shparlinski Igor E.

“…But the modern methods of analytic number theory have – so far – not even allowed to prove that there are infinitely many of them. …”
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Beurling-Selberg extremization and modular bootstrap at high energies by Baur Mukhametzhanov, Sridip Pal

“…The optimization of the bounds over this choice turns out to be exactly the Beurling-Selberg extremization problem, widely known in analytic number theory. We review solutions of this problem and present the corresponding bounds on the number of operators for any $\delta \geq 0$. …”
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