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Showing 1 to 10 of 10 for “"Dirichlet L-functions"”.
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"Mixed joint universality for Dirichlet L-functions and Hurwitz type zeta-functions" /
… thesis are mixed joint universality theorems for Dirichlet L-functions and Hurwitz type zeta-functions, i.e., theorems on simultaneous approximation of a collection of analytic functions by shifts of Dirichlet L-functions which have Euler's product over primes and by shifts of Hurwitz type …
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Explicit Formula for the Mean Square of Dirichlet L-Functions to Prime Power Moduli
<p>Individual values of L-functions inside the critical strip have great arithmetic significance (such as the Riemann hypothesis) but are presently not well-understood. In several important problems in analytic number theory, including how primes are distributed, estimates such as power moments …
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Visibility of lattice points in high dimensional spaces and extreme values of combinations of Dirichlet L-functions
… thesis, we work with large values of certain Dirichlet series and their partial sums. In particular, we examine a `short' partial sum of the Riemann Zeta function, $\zeta_N(s) = \sum_{n\le N}\frac{1}{n^s}$. We obtain large values of $\zeta_N\left(\frac{1}{2}+it\right)$ for $t\in[\sqrt{T}, T]$ …
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Dirichlė L funkcijų ir Hurvico tipo dzeta funkcijų mišrus jungtinis universalumas - santrauka /
… thesis are mixed joint universality theorems for Dirichlet L-functions and Hurwitz type zeta-functions, i.e., theorems on simultaneous approximation of a collection of analytic functions by shifts of Dirichlet L-functions which have Euler's product over primes and by shifts of Hurwitz type …
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Topics in analytic number theory
We investigate properties of prime numbers and L-functions, and interactions between these two topics. First, we discuss the problem of primes in thin sequences, expanding on work of Maynard and Friedlander-Iwaniec. Next, motivated by work of Iwaniec and Sarnak, we study the question of average …
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L-functions and J-spectra
… have studied the twistings of the Riemann ζ-functions and Eisenstein series by Dirichlet characters. We first explain congruences of these twisted Eisenstein series of level Γ_1(N) and character χ via the Dieudonné theory of height 1 formal groups and formal A-modules and their finite …
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Explicit Estimates for Functions of Primes in Arithmetic Progressions
… three topics: Explicit zero-free regions for Dirichlet L-functions, numerical estimates for the error term in the prime number theorem for arithmetic progressions, and Waring's problem for cubes.
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Limit Theorems for L-functions in Analytic Number Theory
… the same rate of convergence in the case of Dirichlet L-functions. Assuming the Riemann hypothesis, we improve the rate of convergence by using an approximation for the logarithm of zeta given by Selberg.</p>
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Topics in analytic number theory
… proves several new theorems concerning L-functions and the distribution of primes. In the first chapter, we establish the first explicit form of the Vinogradov–Korobov zero-free region for Dirichlet L-functions. In the second chapter, we generalize recent work on large gaps between primes …
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Topics in the theory of automorphic L-functions
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01