Results 41 to 50 of about 185 (158)

The second moment of sums of Hecke eigenvalues II

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract Let f$f$ be a holomorphic Hecke cusp form of weight k$k$ for SL2(Z)$\mathrm{SL}_2(\mathbb {Z})$, and let (λf(n))n⩾1$(\lambda _f(n))_{n\geqslant 1}$ denote its sequence of normalised Hecke eigenvalues. We compute the first and second moments of the sums S(x,f)=∑x⩽n⩽2xλf(n)$\mathcal {S}(x,f)=\sum _{x\leqslant n\leqslant 2x} \lambda _f(n)$, on ...
Ned Carmichael
wiley   +1 more source

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
wiley   +1 more source

On the mean value of the mixed exponential sums with Dirichlet characters and general gauss sum [PDF]

, 2013
summary:The main purpose of the paper is to study, using the analytic method and the property of the Ramanujan's sum, the computational problem of the mean value of the mixed exponential sums with Dirichlet characters and general Gauss sum. For integers $
Huaning Liu, Du, Yongguang, Liu, Huaning, Yongguang Du   +3 more
core   +1 more source

Distribution of integer points on determinant surfaces and a mod‐p analogue

Mathematika, Volume 72, Issue 2, April 2026.
Abstract We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form xy−zw=r$xy-zw=r$, where r$r$ is a non‐zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables x,y,z,w$x, y, z, w$ as well as of r$r$.
Satadal Ganguly, Rachita Guria
wiley   +1 more source

New Kloosterman sum identities and equalities over finite fields

, 2008
We present some general equalities between Kloosterman sums over finite fields of arbitrary characteristics.
Xiang, Qing, Hollmann, Henk D.L., Cao, Xiwang, Henk D.L. Hollmann, Xiwang Cao, Qing Xiang   +5 more
core   +1 more source

Bounds and algorithms for the K-Bessel function of imaginary order [PDF]

, 2013
Using the paths of steepest descent, we prove precise bounds with numerical implied constants for the modified Bessel function of imaginary order and its first two derivatives with respect to the order.
Booker, Andrew R, Strömbergsson, Andreas, Then, Holger L, Then, Holger, Booker, Andrew R., Strombergsson, Andreas,   +5 more
core   +1 more source

Drone‐imaging assisted genome‐wide association studies reveal key quantitative trait loci for emergence and late blight resistance in tetraploid potato

Crop Science, Volume 66, Issue 2, March/April 2026.
Abstract Solanum tuberosum L. (potato) is the world's most important vegetable crop, and developing improved cultivars is paramount for global food security. The efficacy of the genomic prediction models that accelerate breeding and genome‐wide association studies (GWAS) depends on large, high‐quality phenotypic datasets, which are often associated ...
Trine Aalborg, Mathias Timmermann Christiansen, Hélène Romé, Aakash Chawade, Merethe Bagge, Kåre Lehmann Nielsen   +5 more
wiley   +1 more source

On character sums over a short interval

, 2009
The main purpose of this paper is using the analytic methods to study the hybrid mean value involving the character sums, general quadratic Gauss sums and general Kloosterman sums, and give several interesting mean value ...
Xu, Zhefeng, Zhang, Tianping, Li, Zhanhu
core   +1 more source

Potato dihaploids uncover diverse alleles to facilitate diploid potato breeding

The Plant Genome, Volume 19, Issue 1, March 2026.
Abstract Commercial potato (Solanum tuberosum) in North America is a clonal autotetraploid crop, which complicates breeding. Efforts are underway to convert potato to a diploid inbred‐hybrid crop, allowing breeders to more quickly meet market and environmental demands.
Sapphire Coronejo, Brieanne Vaillancourt, John P. Hamilton, Xiaoxi Meng, Kathrine Mailloux, Grace Christensen, Jessica Huege, Kathleen M. Shaw, Husain I. Agha, Oluwafemi Alaba, Kristen Brown‐Donovan, James S. Busse, Andy Hamernik, Maria V. Caraza‐Harter, Lucas Heroux, Hemant Balasaheb Kardile, Ericka Knoeck, Peyton L. Sorensen, Diana Spencer, Solomon Yilma, Paul C. Bethke, David Douches, Joshua Parsons, Vidyasagar Sathuvalli, Ek Han Tan, Jeffrey B. Endelman, C. Robin Buell, Laura M. Shannon   +27 more
wiley   +1 more source

A note on the fourth power mean of the generalized Kloosterman sums

Journal of Number Theory, 2017
Let \(p\) be an odd prime, and let \(\alpha\geq 2\) be an integer. Let \(\chi\) be any non-primitive character modulo \(p^{\alpha}\) satisfying \(\chi\neq \chi_0\), the principal character. Let \(n\) be an integer with \((n, p)=1\). This paper proves that \[ \mathop{\sum_{m=1}^{p^{\alpha}}}_{(m,p)=1}\left|\sum_{a=1}^{p^{\alpha}}\chi(a)e\left(\frac{ma+n\
Zhang, Wenpeng, Shen, Shimeng
openaire   +2 more sources