Results 51 to 60 of about 427 (155)
Ramanujan's trigonometric sums and para-orthogonal polynomials on the unit circle [PDF]
, 2021 Alexei Zhedanov
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Triple sums of Kloosterman sums and the discrepancy of modular inverses
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract We investigate the distribution of modular inverses modulo positive integers c$c$ in a large interval. We provide upper and lower bounds for their box, ball, and isotropic discrepancy, thereby exhibiting some deviations from random point sets. The analysis is based, among other things, on a new bound for a triple sum of Kloosterman sums.
Valentin Blomer +2 more
wiley +1 more source
Matrix-Based Ramanujan-Sums Transforms
IEEE Signal Processing Letters, 2013 <p>In this letter, we study the Ramanujan Sums (RS) transform by means of matrix multiplication. The RS are orthogonal in nature and therefore offer excellent energy conservation capability. The 1-D and 2-D forward RS transforms are easy to calculate, but their inverse transforms are not defined in the literature for non-even function . We solved
Chen, Guangyi +2 more
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Canonical Labeling of Latin Squares in Average‐Case Polynomial Time
Random Structures &Algorithms, Volume 66, Issue 4, July 2025.ABSTRACT A Latin square of order n$$ n $$ is an n×n$$ n\times n $$ matrix in which each row and column contains each of n$$ n $$ symbols exactly once. For ε>0$$ \varepsilon >0 $$, we show that with high probability a uniformly random Latin square of order n$$ n $$ has no proper subsquare of order larger than n1/2log1/2+εn$$ {n}^{1/2}{\log}^{1/2 ...
Michael J. Gill +2 more
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Arithmetic constants for symplectic variances of the divisor function
Mathematika, Volume 71, Issue 3, July 2025.Abstract Kuperberg and Lalín stated some conjectures on the variance of certain sums of the divisor function dk(n)$d_k(n)$ over number fields, which were inspired by analogous results over function fields proven by the authors. These problems are related to certain symplectic matrix integrals. While the function field results can be directly related to
Vivian Kuperberg, Matilde Lalín
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Ramanujan’s Tau-Function and Convolution Sums
European Journal of Theoretical and Applied SciencesWe study certain type of convolution sums involving an arbitrary arithmetic function f, which it is applied to Ramanujan’s tau function when f coincides with the sum of divisors function.
R. Sivaraman +2 more
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The urban mine of the Netherlands: The material basis for a circular economy
Journal of Industrial Ecology, Volume 29, Issue 3, Page 967-981, June 2025.Abstract Resources are essential for humanity's well‐being and development. At the same time, resources lay at the heart of many environmental problems. A sustainable resource use facilitates development but reduces environmental problems. This apparent contradiction can be solved by moving toward a circular economy: keeping resources, once extracted ...
Ester van der Voet +7 more
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Lp$L^p$‐norm bounds for automorphic forms via spectral reciprocity
Proceedings of the London Mathematical Society, Volume 130, Issue 6, June 2025.Abstract Let g$g$ be a Hecke–Maaß cusp form on the modular surface SL2(Z)∖H$\operatorname{SL}_2(\mathbb {Z}) \backslash \mathbb {H}$, namely an L2$L^2$‐normalised non‐constant Laplacian eigenfunction on SL2(Z)∖H$\operatorname{SL}_2(\mathbb {Z}) \backslash \mathbb {H}$ that is additionally a joint eigenfunction of every Hecke operator. We prove the L4$L^
Peter Humphries, Rizwanur Khan
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Physiological Reports, Volume 13, Issue 11, June 2025.Hemiparetic cerebral palsy (HCP) results in micro‐ and macro‐structural adaptations in affected forearm muscles, which can be captured by diffusion tensor imaging (DTI) techniques and are related to reduced grip strength. These findings provide the foundation for DTI‐based, non‐invasive biomarkers of musculoskeletal changes following HCP and have ...
Divya Joshi +3 more
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Construction of a repetitive magic square with Ramanujan's number as its product. [PDF]
Heliyon, 2023 Dhandapani PB +2 more
europepmc +1 more source