Bilinear forms in Weyl sums for modular square roots and applications

DOI10.1016/j.aim.2020.107369zbMath1469.11270arXiv1908.10143OpenAlexW3064926101MaRDI QIDQ2213770

Alexandru Zaharescu, Bryce Kerr, Alexander Dunn, Igor E. Shparlinski

Publication date: 3 December 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.10143

zbMATH Keywords

discrepancybinary formsadditive energybilinear sumsmodular square rootsprime quadratic residues

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Estimates on exponential sums (11L07) Sums over primes (11L20) Irregularities of distribution, discrepancy (11K38) Primes represented by polynomials; other multiplicative structures of polynomial values (11N32)

Related Items (7)

Bilinear sums of Gauss sums ⋮ Energy bounds, bilinear forms and their applications in function fields ⋮ Reconstructing points of superelliptic curves over a prime finite field ⋮ On the distribution of modular square roots of primes ⋮ Bounds on bilinear forms with Kloosterman sums ⋮ Products of primes in arithmetic progressions ⋮ A problem in comparative order theory

Cites Work

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• Points on curves in small boxes and applications
• On the residues of products of prime numbers
• Sequences, discrepancies and applications
• Hybrid bounds for quadratic Weyl sums and arithmetic applications
• Hyperbolic distribution problems and half-integral weight Maass forms
• Successive-minima-type inequalities
• The cubic moment of central values of automorphic \(L\)-functions
• Equidistribution of roots of a quadratic congruence to prime moduli
• Entropy of quantum limits
• Zeros of families of automorphic \(L\)-functions close to 1.
• Congruences with intervals and arbitrary sets
• Elliptic curves and lower bounds for class numbers
• Simultaneous non-vanishing for Dirichlet \(L\)-functions
• An explicit bound for the least prime ideal in the Chebotarev density theorem
• Bilinear forms with Kloosterman sums and applications
• On congruences with products of variables from short intervals and applications
• On the discrepancy of uniformly distributed roots of quadratic congruences
• Algebraic trace functions over the primes
• Weyl Sums for Quadratic Roots
• Bounds for the first several prime character nonresidues
• On moments of twisted L-functions
• The distribution of quadratic residues and non‐residues
• Small prime 𝑘th power residues
• Sur le problème des diviseurs de Titchmarsh.
• Prime Twins and Siegel Zeros
• Gauss’ class number problem for imaginary quadratic fields
• Prime Numbers in Short Intervals and a Generalized Vaughan Identity
• The least prime ideal.
• A character-sum estimate and applications
• On short products of primes in arithmetic progressions
• Small prime $k$th power residues for $k=2,3,4$: A reciprocity laws approach
• A mean value estimate for real character sums
• Primes represented by positive definite binary quadratic forms
• Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums
• Reflection Principles and Bounds for Class Group Torsion
• Density of non-residues in Burgess-type intervals and applications
• On Exponential Sums in Finite Fields
• The Least Prime K -th-Power Residue
• Über die Ausnahmenullstelle der Heckeschen L-Funktionen

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