Bounds on bilinear sums of kloosterman sums

Author: ylud

August undefined, 2024

WebThe bounds obtained for these sums are nontrivial for . As a corollary of such bounds, we obtain some new results concerning the distribution of frac- ... the case of a prime q to estimate the bilinear form 1 ... Kloosterman sums,” Nieuw Arch. Wiskunde Ser. 5 4, 380–384 (2000). WebJan 1, 2024 · Bounds on bilinear sums of Kloosterman sums - ScienceDirect Journal of Number Theory Volume 242, January 2024, Pages 102-111 General Section Bounds on …

SOME APPLICATIONS OF SMOOTH BILINEAR FORMS WITH …

WebThe bounds obtained for these sums are nontrivial for . As a corollary of such bounds, we obtain some new results concerning the distribution of frac- ... the case of a prime q to … WebOct 19, 2015 · Bilinear forms with Kloosterman sums. where (1) is a (normalized) hyper-Kloosterman sum (for , this is a classical Kloosterman sum) modulo a prime ; and (2) the ranges and are such that we have non-trivial bounds even if is a bit smaller than in logarithmic scale. In other words, we obtain non-trivial results below the “Pólya … line dance two step forever and ever

Bilinear sums with $GL(2)$ coefficients and the exponent of ...

WebFeb 20, 2024 · The proofs of the above estimates are based on an approach of Blomer combined with some recent bounds on bilinear sums of Kloosterman sums due to … WebKloosterman sums, and prove an extension for correlation sums of Kloosterman sums against Fourier coe cients of modular forms. We use these bounds to improve on earlier … WebKloosterman sums have in recent years played an increasingly important role in the study of many problems in analytic number theory. The Kloosterman sum with character ˜(mod c)is (1:1) S˜(a;b;c)= X x (mod c) ˜(x)e ax + bx c where e(t)=e2ˇit and xx 1 (mod c). If ˜is the principal character this is the classical Kloosterman sum and if ˜(x)= x c line dance two step shuffle

$arXiv:2111.07311v1 [math.NT] 14 Nov 2024$

Sums of Kloosterman sums - Columbia University

WebBOUNDS ON BILINEAR SUMS OF KLOOSTERMAN SUMS NILANJAN BAG AND IGOR E. SHPARLINSKI Abstract. We use some elementary arguments to obtain a new bound … line dance unchain my heartWebJan 1, 2024 · We use some elementary arguments to obtain a new bound on bilinear sums with weighted Kloosterman sums which complements those recently obtained by E. Kowalski, P. Michel and W. Sawin (2024). ... Bounds on bilinear sums of Kloosterman sums. Author links open overlay panel Nilanjan Bag a, Igor E. Shparlinski b. Show more. … hotspot not showing on pc

"WebJan 1, 2024 · We use some elementary arguments to obtain a new bound on bilinear sums with weighted Kloosterman sums which complements those recently obtained by E. … " - Bounds on bilinear sums of kloosterman sums

Bounds on bilinear sums of kloosterman sums

[1411.4467] On moments of twisted $L$-functions - arXiv.org

WebNov 17, 2014 · On moments of twisted. -functions. We study the average of the product of the central values of two -functions of modular forms and twisted by Dirichlet characters to a large prime modulus . As our principal tools, we use spectral theory to develop bounds on averages of shifted convolution sums with differences ranging over multiples of , and ... WebBILINEAR FORMS WITH KLOOSTERMAN SUMS AND APPLICATIONS EMMANUEL KOWALSKI, PHILIPPE MICHEL, AND WILLIAM F. SAWIN Abstract. We prove non …

Did you know?

WebApr 11, 2024 · Bounds on bilinear forms with Kloosterman sums Authors: Bryce Kerr Igor E. Shparlinski UNSW Sydney Xiaosheng Wu PING XI Xi'an Jiaotong University Preprints … WebKloosterman sums, Kloosterman sheaves, Riemann Hypothesis over nite elds, random Fourier series, short exponential sums, probability in Banach spaces. ... As an application of Theorems1.3and1.5, we will obtain fairly sharp bounds for the probability of large values of partial sums of the corresponding families of exponential sums: Theorem 1.6 ...

WebHowever, there has been very little work done in this area in the setting of rational function fields over finite fields. We remedy this and provide a number of new non-trivial bounds for bilinear forms of Kloosterman and Gauss sums in this setting, based on new bounds on the number of solutions to certain modular congruences in $\mathbb{F}_q[T]$ . WebBILINEAR FORMS WITH KLOOSTERMAN SUMS AND APPLICATIONS EMMANUEL KOWALSKI, PHILIPPE MICHEL, AND WILL SAWIN Abstract. We prove non-trivial …

WebMar 24, 2024 · Kloosterman's sum is defined by S(u,v,n)=sum_(h)exp[(2pii(uh+vh^_))/n], (1) where h runs through a complete set of residues relatively prime to n and h^_ is … WebApr 11, 2024 · Bilinear forms with Kloosterman and Gauss sums in function fields. In recent years, there has been a lot of progress in obtaining non-trivial bounds for bilinear forms of Kloosterman sums in for arbitrary integers . These results have been motivated by a wide variety of applications, such as improved asymptotic formulas for moments of ...

WebFloating normalization parameters in regressions allow incorporation of prior knowledge, such as a known analytic behavior and/or a known value at a kinematic endpoint. Unfortunately, there is often no unique way to make use of this prior knowledge, and thus, different analysis choices can lead to very different normalization parameters and …

WebWe obtain the exponent of distribution $1/2+1/30$ for the ternary divisor function $d_3$ to square-free and prime power moduli, improving the previous results of ... linedance two waysWebBILINEAR FORMS WITH KLOOSTERMAN SUMS 415 of this construction), which explains why they occur after applying the Voronoi summation formula on GL k. Our main results provide new bounds for general bilinear forms in hyper-Kloosterman sums that go beyond the Fourier-theoretic range; seeTheorems 1.1and1.3below. linedance uptown funk abWebBilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions. ... Bounds on bilinear forms with Kloosterman sums. B Kerr, IE Shparlinski, X Wu, P Xi. arXiv preprint arXiv:2204.05038, 2024. 2: 2024: hotspot not showing in available networksWebWe prove new bounds on bilinear forms with Kloosterman sums, complementing and improving a series of results by \'E. Fouvry, E. Kowalski and Ph. Michel (2014), V. Blomer, \'E. Fouvry, E. Kowalski, Ph. hotspot not turning on windows 11Web- the hyper-Kloosterman sums are constructed by iterated multiplicative convolution (see Katz’s book [20] for the algebro-geometric version of this construction), which explains why they occur after applying the Voronoi summation formula on GL k. Our main results provide new bounds for general bilinear forms in hyper-Kloosterman sums that line dance up \\u0026 down the countryWebBilinear forms with Kloosterman sums and applications By Emmanuel Kowalski, Philippe Michel, and Will Sawin Dedicated to Henryk Iwaniec Abstract We prove nontrivial … line dance unlock my heartWebThese improvements rely on new estimates for Type II bilinear forms with incomplete Kloosterman sums. We also establish new estimates for bilinear forms with one … line dance under the boardwalk