Results 21 to 30 of about 42 (38)
Fourier expansions of complex‐valued Eisenstein series on finite upper half planes
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We consider complex‐valued modular forms on finite upper half planes Hq and obtain Fourier expansions of Eisenstein series invariant under the groups Γ=SL(2,Fp) and GL(2,Fp). The expansions are analogous to those of Maass wave forms on the ordinary Poincaré upper half plane —the K‐Bessel functions being replaced by Kloosterman sums.
Anthony Shaheen, Audrey Terras
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Non‐vanishing of Poincaré series on average
Mathematika, Volume 72, Issue 2, April 2026.Abstract We study when Poincaré series for congruence subgroups do not vanish identically. We show that almost all Poincaré series with suitable parameters do not vanish when either the weight k$k$ or the index m$m$ varies in a dyadic interval. Crucially, analyzing the problem ‘on average’ over these weights or indices allows us to prove non‐vanishing ...
Ned Carmichael, Noam Kimmel
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Differences between powers of a primitive root
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 6, Page 325-331, 2002., 2002 We study the set of differences {gx − gy(modp) : 1 ≤ x, y ≤ N} where p is a large prime number, g is a primitive root (modp), and p2/3 < N < p.
Marian Vâjâitu, Alexandru Zaharescu
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An asymptotic local–global theorem on heights of some Kleinian group orbits
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We prove an asymptotic local–global theorem on the heights of point orbits of thin subgroups of Bianchi groups in H3$\mathbb {H}^3$.
Xuanxuan Xiao, Xin Zhang
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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
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Some New Identities Related to Dedekind Sums Modulo a Prime
Journal of Mathematics, Volume 2024, Issue 1, 2024.The main purpose of this article is to use some identities of the classical Gauss sums, the properties of character sums, and Dedekind sums (modulo an odd prime) to study the computational problem of one‐kind mean values related to Dedekind sums and give some interesting identities for them.
Jiayuan Hu, Xiaogang Liu
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Journal of Mathematics, Volume 2024, Issue 1, 2024.The primary contribution of this paper is to research one kind special Kloosterman sums using analytic method. We translate one kind fourth power mean of the Kloosterman sums into the character sums of one kind polynomials. It is possible to construct an exact formula for the fourth power mean of one kind Kloosterman sums by computing the character ...
Shushu Ning, Xuexia Wang, Ming-Sheng Liu
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