ON THE EXPONENT OF DISTRIBUTION OF THE TERNARY DIVISOR FUNCTION

DOI10.1112/S0025579314000096zbMath1317.11080arXiv1304.3199MaRDI QIDQ5179256

Étienne Fouvry, Philippe Michel, Emmanuel Kowalski

Publication date: 19 March 2015

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.3199

zbMATH Keywords

arithmetic progressionstrace functionsVoronoi formulaKloostermaniaexponential sums over finite fieldsexponent of distributionternary divisor function

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Exponential sums (11T23) Gauss and Kloosterman sums; generalizations (11L05) Distribution of integers with specified multiplicative constraints (11N25)

Related Items (25)

Cancellation in algebraic twisted sums on \(\operatorname{GL}_m\) ⋮ Some applications of smooth bilinear forms with Kloosterman sums ⋮ TERNARY DIVISOR FUNCTIONS IN ARITHMETIC PROGRESSIONS TO SMOOTH MODULI ⋮ Bilinear forms with Kloosterman sums and applications ⋮ Multiplicative functions in short arithmetic progressions ⋮ On short sums of trace functions ⋮ Divisor problem in arithmetic progressions modulo a prime power ⋮ A study in sums of products ⋮ On algebraic twists with composite moduli ⋮ Bilinear sums with GL(2)$GL(2)$ coefficients and the exponent of distribution of d3$d_3$ ⋮ Bounds on bilinear forms with Kloosterman sums ⋮ Rankin-Selberg coefficients in large arithmetic progressions ⋮ Algebraic twists of GL3 × GL2 L-functions ⋮ Variance of sums in arithmetic progressions of divisor functions associated with higher degree L-functions in 𝔽q[t] ⋮ The Bombieri-Vinogradov theorem for nilsequences ⋮ Counting primes ⋮ Sums of divisor functions in \(\mathbb {F}_q[t\) and matrix integrals] ⋮ Lectures on applied ℓ-adic cohomology ⋮ Generalized divisor functions in arithmetic progressions: I. ⋮ On the conductor of cohomological transforms ⋮ PERIODIC TWISTS OF -AUTOMORPHIC FORMS ⋮ Bounds on average values of double incomplete Kloosterman sums ⋮ Algebraic twists of modular forms and Hecke orbits ⋮ Multiplicative functions in large arithmetic progressions and applications ⋮ The Second Moment Theory of Families of 𝐿-Functions–The Case of Twisted Hecke 𝐿-Functions

Cites Work

• Primes in arithmetic progressions to large moduli. II
• Around the Bombieri-Vinogradov theorem
• Incomplete Kloosterman sums and a divisor problem. Appendix: On some exponential sums by Bryan J. Birch and Enrico Bombieri
• Primes in arithmetic progressions to large moduli
• Kloosterman sums and Fourier coefficients of cusp forms
• Bounded gaps between primes
• Über die mittlere Verteilung der Werte zahlentheoretischer Funktionen auf Restklassen. I
• An induction principle for the generalization of Bombieri's prime number theorem

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