Results 41 to 50 of about 427 (155)

Character sum, reciprocity, and Voronoi formula

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3797-3823, December 2025.
Abstract We prove a novel four‐variable character sum identity that serves as a twisted, non‐Archimedean analog of Weber's integrals for Bessel functions. Using this identity and ideas from Venkatesh's thesis, we provide a short spectral proof of the Voronoi formulae for classical modular forms with character twists.
Chung‐Hang Kwan, Wing Hong Leung
wiley   +1 more source

Poisson kernels of q$q$‐3D Hermite polynomials expansion for functions of several variables via generalized q$q$‐heat equations

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract The representation of an analytic function as a series involving q$q$‐polynomials is a fundamental problem in classical analysis and approximation theory [Ramanujan J. 19 (2009), no. 3, 281–303]. In this paper, our investigation is focusing on q$q$‐analog complex Hermite polynomials, which were motivated by Ismail and Zhang [Adv. Appl.
Jian Cao
wiley   +1 more source

Ramanujan sums and rectangular power sums

Journal of Pure and Applied Algebra
For a fixed nonnegative integer $u$ and positive integer $n$, we investigate the symmetric function \[\sum_{d|n} \left(c_d(\tfrac{n}{d})\right)^u p_d^{\tfrac{n}{d}},\] where $p_n$ denotes the $n$th power sum symmetric function, and $c_d(r)$ is a Ramanujan sum, equal to the sum of the $r$th powers of all the primitive $d$th roots of unity. We establish
John Shareshian, Sheila Sundaram
openaire   +2 more sources

Decision‐making between DCA and VMAT in Linac‐based SRS for brain lesions: A dosimetric analysis based on tumor size and geometry and introduction of Qasym

Journal of Applied Clinical Medical Physics, Volume 26, Issue 11, November 2025.
Abstract Introduction Linac‐based SRS provides a highly precise noninvasive treatment option for intracranial lesions. DCA and VMAT are commonly used Linac‐based techniques. There are no standardized guidelines for technique selection, particularly considering the geometric properties of the lesions.
Lara Caglayan, Davide Scafa, Patrick Eich, Christina Leitzen, Fabian Kugel, Stephan Garbe, Gustavo Renato Sarria, Christos Moustakis, Dimos Baltas, Julian Philipp Layer, Cas Stefaan Dejonckheere, Andrea Renate Glasmacher, Shari Wiegreffe, Anca L Grosu, Eleni Gkika, Youness Nour   +15 more
wiley   +1 more source

Rankin-Cohen brackets on quasimodular forms [PDF]

, 2008
We give the algebra of quasimodular forms a collection of Rankin-Cohen operators. These operators extend those defined by Cohen on modular forms and, as for modular forms, the first of them provide a Lie structure on quasimodular forms. They also satisfy
Martin, François, Royer, Emmanuel
core   +3 more sources

Soft bounds for local triple products and the subconvexity‐QUE implication for GL2$\mathrm{GL}_2$

Mathematika, Volume 71, Issue 4, October 2025.
Abstract We give a soft proof of a uniform upper bound for the local factors in the triple product formula, sufficient for deducing effective and general forms of quantum unique ergodicity (QUE) from subconvexity.
Paul D. Nelson
wiley   +1 more source

On some equations concerning quantum electrodynamics coupled to quantum gravity, the gravitational contributions to the gauge couplings and quantum effects in the theory of gravitation: mathematical connections with some sector of String Theory and Number Theory [PDF]

, 2010
This paper is principally a review, a thesis, of principal results obtained from various authoritative theoretical physicists and mathematicians in some sectors of theoretical physics and mathematics.
Nardelli, Michele
core   +1 more source

Critical Assessment of Contact Resistance and Mobility in Tin Perovskite Field‐Effect Transistors

Advanced Electronic Materials, Volume 11, Issue 15, September 18, 2025.
Contact resistance and field‐effect transistor (FET) mobility of Cs0.15FA0.85SnI3 tin perovskites are determined using gated four‐point‐probe (4PP) FET measurements in a Hall bar geometry. The results indicate that contact resistance can significantly impact transistor characteristics, often leading to underestimation or overestimation of FET mobility ...
Youcheng Zhang, Stefano Pecorario, Xian Wei Chua, Xinglong Ren, Cong Zhao, Rozana Mazlumian, Satyaprasad P. Senanayak, Krishanu Dey, Samuel D. Stranks, Henning Sirringhaus   +9 more
wiley   +1 more source

Uncovering Ramanujan's "Lost" Notebook: An Oral History

, 2012
Here we weave together interviews conducted by the author with three prominent figures in the world of Ramanujan's mathematics, George Andrews, Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the "lost" notebook, Andrews and Berndt'
B.C. Berndt, B.C. Berndt, B.C. Berndt, D.A.B. Young, E.T. Whittaker, G.E. Andrews, G.E. Andrews, G.E. Andrews, G.H. Hardy, K. Bringmann, K. Ono, Robert P. Schneider, S. Ramanujan, W.W.R. Ball   +13 more
core   +1 more source

Correlations of the squares of the Riemann zeta function on the critical line

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract We compute the average of a product of two shifted squares of the Riemann zeta function on the critical line with shifts up to size T3/2−ε$T^{3/2-\varepsilon }$. We give an explicit expression for such an average and derive an approximate spectral expansion for the error term similar to Motohashi's.
Valeriya Kovaleva
wiley   +1 more source