Results 51 to 60 of about 859,926 (192)
Sums of SL(3,Z) Kloosterman Sums [PDF]
, 2012 We show that sums of the SL(3,Z) long element Kloosterman sum against a smooth weight function have cancellation due to the variation in argument of the Kloosterman sums, when each modulus is at least the square root of the other.
Buttcane, Jack
core
Upper bounds on n-dimensional Kloosterman sums [PDF]
, 2004 Let pm be any prime power and Kn(a,pm) be the Kloosterman sum , where the xi are restricted to values not divisible by p. Let m,n be positive integers with m2 and suppose that pγ||(n+1).
Liu, Ming-Chit +5 more
core +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
Airy Sums, Kloosterman Sums, and Salié Sums
Journal of Number Theory, 1997 In 1993 \textit{W. Duke} and \textit{H. Iwaniec} proved that a certain class of cubic exponential sums can be expressed through Kloosterman sums twisted by a cubic character [Contemp. Math. 143, 255-258 (1993; Zbl 0792.11029)]. Their proof made use of one of the Davenport-Hasse theorems.
openaire +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
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 +5 more
wiley +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 +27 more
wiley +1 more source
On sums of Kloosterman and Gauss sums
Transactions of the American Mathematical Society, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
Kloosterman sums with multiplicative coefficients [PDF]
Izvestiya: Mathematics, 2018 The series of some new estimates for the sums of the type \[ S_{q}(x;f)\,=\,\mathop{{\sum}'}\limits_{n\leqslant x}f(n)e_{q}(an^{*}+bn) \] is obtained. Here $q$ is a sufficiently large integer, $\sqrt{q}(\log{q})\!\ll\!x\leqslant q$, $a,b$ are integers, $(a,q)=1$, $e_{q}(v) = e^{2πiv/q}$, $f(n)$ is a multiplicative function, $nn^{*}\equiv 1 \pmod{q ...
openaire +3 more sources
On the distribution of angles of Kloosterman sums.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1989 Let \({\mathbb{F}}_ q\) denote the finite field with q elements where q is a prime power. For \(\lambda \in {\mathbb{F}}_ q^{\times}\) let \(\theta\) (q,\(\lambda)\) be the unique angle defined by a certain Kloosterman sum. In this paper the author applies results due to \textit{P. Deligne} [Publ. Math., Inst. Hautes Étud. Sci.
openaire +2 more sources