On algebraic degrees of certain exponential sums over finite fields
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Xin Lin
Abstract
From a complex perspective, Birch and Bombieri (1985) proposed the study of an important class of n-dimensional exponential sums for
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 12301010
Funding statement: Xin Lin is supported by the National Natural Science Foundation of China (No. 12301010).
References
[1] B. J. Birch and E. Bombieri, Appendix: On some exponential sums, Ann. of Math. (2) 121 (1985), no. 2, 345–350. 10.2307/1971176Search in Google Scholar
[2] C. Chen and X. Lin, L-functions of certain exponential sums over finite fields, Math. Z. 300 (2022), no. 2, 1851–1871. 10.1007/s00209-021-02843-2Search in Google Scholar
[3] P. Deligne, La conjecture de Weil. II, Publ. Math. Inst. Hautes Études Sci. 52 (1980), 137–252. 10.1007/BF02684780Search in Google Scholar
[4] B. Dwork, Bessel functions as p-adic functions of the argument, Duke Math. J. 41 (1974), 711–738. 10.1215/S0012-7094-74-04176-3Search in Google Scholar
[5] J. B. Friedlander and H. Iwaniec, Incomplete Kloosterman sums and a divisor problem, Ann. of Math. (2) 121 (1985), no. 2, 319–344. 10.2307/1971175Search in Google Scholar
[6]
D. R. Heath-Brown,
The divisor function
[7] N. M. Katz, On a certain class of exponential sums, J. Reine Angew. Math. 377 (1987), 12–17. 10.1515/crll.1987.377.12Search in Google Scholar
[8] X. Lin and C. Chen, L-functions of certain exponential sums over finite fields II, J. Number Theory 241 (2022), 198–220. 10.1016/j.jnt.2022.03.006Search in Google Scholar
[9] X. Lin and D. Wan, On algebraic degrees of inverted Kloosterman sums, Finite Fields Appl. 99 (2024), Article ID 102477. 10.1016/j.ffa.2024.102477Search in Google Scholar
[10] S. Sperber, Congruence properties of the hyper-Kloosterman sum, Compos. Math. 40 (1980), no. 1, 3–33. Search in Google Scholar
[11] D. Wan, Minimal polynomials and distinctness of Kloosterman sums, Finite Fields Appl. 1 (1995), 189–203. 10.1006/ffta.1995.1015Search in Google Scholar
[12] L. Yang, Degrees of generalized Kloosterman sums, Forum Math. 36 (2024), no. 6, 1659–1665. Search in Google Scholar
[13] Y. Zhang, Bounded gaps between primes, Ann. of Math. (2) 179 (2014), no. 3, 1121–1174. 10.4007/annals.2014.179.3.7Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Rings of differential operators on (k,s)-th Tjurina algebras of singularities
- Cokernels of random matrix products and flag Cohen–Lenstra heuristic
- Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
- The L p -L q compactness of commutators of oscillatory singular integrals
- Determination of a pair of newforms from the product of their twisted central values
- Metrical properties of exponentially growing partial quotients
- Nonlinear operations and factorizations on a class of affine modulation spaces
- On algebraic degrees of certain exponential sums over finite fields
- The ranks of (a,b)-Fibonacci sequences and congruences for certain partition functions and Ramanujan's mock theta functions
- Dynamics of radial threshold solutions for generalized energy-critical Hartree equation
- Modular representations of GL2(𝔽𝑞) using calculus
- Bounding the number of p'-degree characters from below
- Existence and multiplicity of non-radial sign-changing solutions for a semilinear elliptic equation in hyperbolic space
- Duality theorems for polyanalytic functions
- Lower bounds for the number of number fields with Galois group GL2(𝔽ℓ)
- Cylindrical ample divisors on Du Val del Pezzo surfaces
Articles in the same Issue
- Frontmatter
- Rings of differential operators on (k,s)-th Tjurina algebras of singularities
- Cokernels of random matrix products and flag Cohen–Lenstra heuristic
- Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
- The L p -L q compactness of commutators of oscillatory singular integrals
- Determination of a pair of newforms from the product of their twisted central values
- Metrical properties of exponentially growing partial quotients
- Nonlinear operations and factorizations on a class of affine modulation spaces
- On algebraic degrees of certain exponential sums over finite fields
- The ranks of (a,b)-Fibonacci sequences and congruences for certain partition functions and Ramanujan's mock theta functions
- Dynamics of radial threshold solutions for generalized energy-critical Hartree equation
- Modular representations of GL2(𝔽𝑞) using calculus
- Bounding the number of p'-degree characters from below
- Existence and multiplicity of non-radial sign-changing solutions for a semilinear elliptic equation in hyperbolic space
- Duality theorems for polyanalytic functions
- Lower bounds for the number of number fields with Galois group GL2(𝔽ℓ)
- Cylindrical ample divisors on Du Val del Pezzo surfaces
