Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Ben Kane"'
Autor:
KATHRIN BRINGMANN, BEN KANE
Publikováno v:
Forum of Mathematics, Sigma, Vol 8 (2020)
We start by recalling the following theorem of Rohrlich [17]. To state it, let $\unicode[STIX]{x1D714}_{\mathfrak{z}}$ denote half of the size of the stabilizer $\unicode[STIX]{x1D6E4}_{\mathfrak{z}}$ of $\mathfrak{z}\in \mathbb{H}$ in $\text{SL}_{2}
Externí odkaz:
https://doaj.org/article/40625cbe6cc84b92a0e4dd6a2ddf2583
Publikováno v:
Transactions of the American Mathematical Society. 376:1625-1652
In this paper, we investigate the interplay between positive-definite integral ternary quadratic forms and class numbers. We generalize a result of Jones relating the theta function for the genus of a quadratic form to the Hurwitz class numbers, obta
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7c16a27708a855d3f7d9fdddb3eaa301
https://doi.org/10.1090/tran/8814
https://doi.org/10.1090/tran/8814
Publikováno v:
Transactions of the American Mathematical Society, Series B. 8:615-634
Many papers have studied inequalities for partition functions. Recently, a number of papers have considered mixtures between additive and multiplicative behavior in such inequalities. In particular, Chern–Fu–Tang and Heim–Neuhauser gave conject
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::788aa2f708868c0e6a4775ab10414fe8
https://doi.org/10.1090/btran/77
https://doi.org/10.1090/btran/77
Autor:
Soumyarup Banerjee, Manav Batavia, Sagnik Saha, Ben Kane, Muratzhan Kyranbay, Piyush Varyani, Hiu Chun So, Dayoon Park
Publikováno v:
Journal of Number Theory. 220:163-181
Text In this paper, we consider sums of generalized polygonal numbers with repeats, generalizing Fermat's polygonal number theorem which was proven by Cauchy. In particular, we obtain the minimal number of generalized m-gonal numbers required to repr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c00b918f9a12b36a45a87b4c6295ed17
https://doi.org/10.1016/j.jnt.2020.05.024
https://doi.org/10.1016/j.jnt.2020.05.024
Publikováno v:
Proceedings of the London Mathematical Society. 120:742-769
Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of $L$-functions. In particular, we find finite formulas for certain twisted central $L$-values of a family of elliptic curves in terms o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1640cfc389ecaf661697997754e9015b
https://doi.org/10.1112/plms.12305
https://doi.org/10.1112/plms.12305
Publikováno v:
The Quarterly Journal of Mathematics. 70:1181-1207
In this paper, we study polar harmonic Maass forms of negative integral weight. Using work of Fay, we construct Poincaré series which span the space of such forms and show that their elliptic coefficients exhibit duality properties which are similar
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e19db7a5e54fde94aaea2e431ac3f5a7
https://doi.org/10.1093/qmath/haz009
https://doi.org/10.1093/qmath/haz009
Publikováno v:
Research in Number Theory. 7
In this paper, we investigate sign changes of Fourier coefficients of half-integral weight cusp forms. In a fixed square class $$t\mathbb {Z}^2$$ , we investigate the sign changes in the $$tp^2$$ -th coefficient as p runs through the split or inert p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4c01e90d0853036f8fa03f228b473fc6
https://doi.org/10.1007/s40993-020-00235-9
https://doi.org/10.1007/s40993-020-00235-9
Autor:
Kathrin Bringmann, Ben Kane
In this paper, we construct a family of generalized $L$-functions, one for each point $z$ in the upper half-plane. We prove that as $z$ approaches $i\infty$, these generalized $L$-functions converge to an $L$-function which can be written in terms of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ec86a8f5c5b2209cad937b942db0740e
Publikováno v:
Acta Arithmetica
In this paper, we obtain explicit formulas for the second moments for Hurwitz class numbers $H(4n-t^2)$ with $t$ running through a fixed congruence class modulo $3$.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::87995c3a00f6ac09577eaf051ca9a786
Autor:
Ben Kane, Sudhir Pujahari
In this paper, we study moments of Hurwitz class numbers associated to imaginary quadratic orders restricted into fixed arithmetic progressions. In particular, we fix t t in an arithmetic progression t ≡ m ( mod M ) t\equiv m\ \, \left ( \operatorn
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ecac08b22e5458b157808848235fdcca
http://arxiv.org/abs/2010.15325
http://arxiv.org/abs/2010.15325