Titlebook: Number Theory and Related Fields; In Memory of Alf van Jonathan M. Borwein,Igor Shparlinski,Wadim Zudilin Conference proceedings 2013 Sprin

强有力

Continued Fractions and Dedekind Sums for Function Fields,continued fractions, Hickerson answered these questions affirmatively. In function fields, there exists a Dedekind sum .(., .) (see Sect. 4) similar to .(., .). Using continued fractions, we answer the analogous problems for .(., .).

抵押贷款

中止

defendant

胶状

Some Notes on Weighted Sum Formulae for Double Zeta Values, to new evaluations of sums involving the harmonic numbers, the alternating double zeta values, and the Mordell–Tornheim double sum. We discuss a heuristic for finding or dismissing the existence of similar simple sums. We also produce some new sums from recursions involving the Riemann zeta and the Dirichlet beta functions.

讥讽

Accrue

LUMEN

,Burgess’s Bounds for Character Sums,Let . be a character sum to modulus .. Then the standard Burgess bound takes the form ., where .. We show that . for any positive integers .. ≤ . spaced at least . apart, so that even reducing to a single term of the sum recovers the Burgess estimate.

红润

Overthrow

Families of Cubic Thue Equations with Effective Bounds for the Solutions,To each nontotally real cubic extension . of . and to each generator . of the cubic field ., we attach a family of cubic Thue equations, indexed by the units of ., and we prove that this family of cubic Thue equations has only a finite number of integer solutions, by giving an effective upper bound for these solutions.