This is the author’s version of the paper. The final publication has appeared in J. Number Theory), 2214–2225. A Bombieri-Vinogradov type exponential sum result with applications Kaisa Matom¨aki

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ON THE NUMBER OF SUBSEQUENCES WITH GIVEN SUM OF SEQUENCES IN FINITE ABELIAN p-GROUPS WEIDONG GAO AND ALFRED GEROLDINGER Abstract. Let G be an additive finite abelian p-group. For a given (long) sequence S in G and some e

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• Topological groups
• Abelian group
• Niels Henrik Abel
• Free abelian group
• Center
• Ring theory
• Homological algebra
• Representation theory of finite groups
• Exponential map
• Abstract algebra
• Algebra
• Group theory

Statistics 583, Problem Set 1 Solutions Wellner; [removed]Pn 1. Let SN = i=1 Qi be the Wilcoxon rank sum statistic derived in class on 30

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• Exponentials
• Combinatorics
• Integer sequences
• Exponentiation
• Order statistic
• Factorial
• Central limit theorem
• Exponential family
• Mathematics
• Statistics
• Mathematical analysis

Exponential and Logarithmic Functions Algebra of Functions Sum (f

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• Logarithms
• Exponentials
• Binary operations
• Logarithm
• Natural logarithm
• Inverse function
• Continuous function
• Exponential function
• Injective function
• Mathematics
• Mathematical analysis
• Functions and mappings

Open Problems on Exponential and Character Sums Igor E. Shparlinski Department of Computing, Macquarie University Sydney, NSW 2109, Australia [removed]

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• Number theory
• Kloosterman sum
• Anatolii Alexeevitch Karatsuba
• Arithmetic function
• Character sum
• Exponential sum
• Prime number
• Prime-counting function
• Finite field
• Analytic number theory
• Mathematics
• Mathematical analysis

IMPERIAL COLLEGE LONDON DEPARTMENT OF MATHEMATICS BASIC TECHNIQUES SECTION A: 1) Sum of series: arithmetic and geometric progressions summed to n terms; sum of geometric series; exponential series.

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• Integration by parts
• Sine
• Binomial theorem
• Complex number
• Inverse trigonometric functions
• Mathematical fallacy
• Differential equation
• Plus-minus sign
• Trigonometric functions
• Mathematics
• Trigonometry
• Mathematical analysis

Improved Exponential-time Algorithms for Inhomogeneous-SIS Shi Bai1 , Steven D. Galbraith1 , Liangze Li2 , and Daniel Sheffield1 1 Department of Mathematics, University of Auckland, Auckland, New Zealand. 2

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• Modular arithmetic
• Dynamic programming
• Subset sum problem
• NP
• Chinese remainder theorem
• Euclidean algorithm
• Mathematics
• Theoretical computer science
• Applied mathematics

Trace and Norm L-functions Antonio Rojas Leon Departamento de Álgebra, Universidad de Sevilla Spain Exponential sums de…ned over the rational points of an algebraic variety over a …nite …eld have been extensively

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• Exponential sum
• Exponentials
• Abstract algebra
• Algebraic geometry
• Homological algebra
• Conjectures
• Analytic number theory
• Mathematical analysis
• Mathematics

On SL2(Z) and SL3(Z) Kloosterman sums Olga Balkanova Erasmus Mundus Master ALGANT University of Bordeaux 1

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• Complex analysis
• Kloosterman sum
• Modular form
• Möbius transformation
• Hendrik Kloosterman
• Holomorphic function
• Modular group
• Riemann hypothesis
• Exponential sum
• Mathematical analysis
• Analytic number theory
• Mathematics

DABOUSSI’S VERSION OF VINOGRADOV’S BOUND FOR THE EXPONENTIAL SUM OVER PRIMES (slightly simplified) Notes by Tim Jameson (recalled on a busman’s holiday in Oslo, [removed]Vinogradov’s method to estimate an exponenti

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• Operator theory
• Complex analysis
• Logarithms
• Exponentiation
• Lerch zeta function
• Vertex operator algebra
• Mathematical analysis
• Mathematics
• Abstract algebra