Recent Studies in Number Theory and Algebraic Geometry

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "B: Geometry and Topology".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 413

Special Issue Editor


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Guest Editor
Department of Mathematics, University of York, York, UK
Interests: number theory; elimination theory; transcendence theory; algebraic geometry; diophantine approximations; metric number theory and diophantine approximation; Arakelov’s geometry; geometry of numbers; measure and probability theory; ergodic theory; dynamical systems

Special Issue Information

Dear Colleagues,

This Special Issue, titled “Recent Studies in Number Theory and Algebraic Geometry”, invites contributions that highlight significant recent advancements and emerging trends in these interconnected fields. We are particularly interested in research focusing on analytic number theory, arithmetic geometry, Diophantine approximations, interactions of number theory with other disciplines, and multifractal analysis related to number theory.

This Special Issue will emphasize the diverse approaches and techniques that drive recent progress in number theory, fostering cross-disciplinary dialogue and innovation. Also, any kind of novel and interesting research within the fields of number theory and algebraic geometry are welcome.

Dr. Evgeniy Zorin
Guest Editor

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Keywords

  • analytic number theory
  • arithmetic geometry
  • diophantine approximations
  • interactions of number theory
  • multifractal analysis
  • computational results

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Published Papers (1 paper)

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Research

16 pages, 294 KiB  
Article
On Some Mean Value Results for the Zeta-Function and a Rankin–Selberg Problem
by Jing Huang, Yukun Liu and Deyu Zhang
Mathematics 2025, 13(16), 2681; https://doi.org/10.3390/math13162681 - 20 Aug 2025
Viewed by 145
Abstract
Denote by Δ1(x;φ) the error term in the classical Rankin–Selberg problem. Denote by ζ(s) the Riemann zeta-function. We establish an upper bound for this integral [...] Read more.
Denote by Δ1(x;φ) the error term in the classical Rankin–Selberg problem. Denote by ζ(s) the Riemann zeta-function. We establish an upper bound for this integral 0TΔ1(t;φ)ζ12+it2dt. In addition, when 2k4 is a fixed integer, we will derive an asymptotic formula for the integral 1TΔ1k(t;φ)ζ12+it2dt. The results rely on the power moments of Δ1(t;φ) and E(t), the classical error term in the asymptotic formula for the mean square of ζ12+it. Full article
(This article belongs to the Special Issue Recent Studies in Number Theory and Algebraic Geometry)
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