The Experts below are selected from a list of 3435 Experts worldwide ranked by ideXlab platform

Artur Kawalec - One of the best experts on this subject based on the ideXlab platform.

  • on the complex magnitude of dirichlet beta function
    arXiv: Number Theory, 2020
    Co-Authors: Artur Kawalec
    Abstract:

    In this article, we derive an expression for the complex magnitude of the Dirichlet beta function $\beta(s)$ represented as a Euler prime product and compare with similar results for the Riemann zeta function. We also obtain formulas for $\beta(s)$ valid for an even and odd $k$th positive Integer Argument and present a set of generated formulas for $\beta(k)$ up to $11$th order, including Catalan's constant and compute these formulas numerically. Additionally, we derive a second expression for the complex magnitude of $\beta(s)$ valid in the critical strip from which we obtain a formula for the Euler-Mascheroni constant expressed in terms of zeros of the Dirichlet beta function on the critical line. Finally, we investigate the asymptotic behavior of the Euler prime product on the critical line.

  • prime product formulas for the riemann zeta function and related identities
    arXiv: General Mathematics, 2019
    Co-Authors: Artur Kawalec
    Abstract:

    In this article, we derive a Euler prime product formula for the magnitude of the Riemann zeta function $\zeta(s)$ valid for $\Re(s)>1$, as well as similar formulas for $\zeta(s)$ valid for an even and odd $k$th positive Integer Argument. We shall further give a set of generated formulas for $\zeta(k)$ up to $11$th order, including Apery's constant, and also construct formulas for $\zeta(3/2)$. We'll also validate these formulas numerically.

Kawalec Artur - One of the best experts on this subject based on the ideXlab platform.

  • On the complex magnitude of Dirichlet beta function
    2020
    Co-Authors: Kawalec Artur
    Abstract:

    In this article, we derive an expression for the complex magnitude of the Dirichlet beta function $\beta(s)$ represented as a Euler prime product and compare with similar results for the Riemann zeta function. We also obtain formulas for $\beta(s)$ valid for an even and odd $k$th positive Integer Argument and present a set of generated formulas for $\beta(k)$ up to $11$th order, including Catalan's constant and compute these formulas numerically. Additionally, we derive a second expression for the complex magnitude of $\beta(s)$ valid in the critical strip from which we obtain a formula for the Euler-Mascheroni constant expressed in terms of zeros of the Dirichlet beta function on the critical line. Finally, we investigate the asymptotic behavior of the Euler prime product on the critical line.Comment: 2 Figures, 2 Table

  • Prime product formulas for the Riemann zeta function and related identities
    2019
    Co-Authors: Kawalec Artur
    Abstract:

    In this article, we derive a Euler prime product formula for the magnitude of the Riemann zeta function $\zeta(s)$ valid for $\Re(s)>1$, as well as similar formulas for $\zeta(s)$ valid for an even and odd $k$th positive Integer Argument. We shall further give a set of generated formulas for $\zeta(k)$ up to $11$th order, including Ap\'ery's constant, and also construct formulas for $\zeta(3/2)$. We'll also validate these formulas numerically.Comment: 7 Pages, 1 Tabl

Beshenov A. - One of the best experts on this subject based on the ideXlab platform.

  • Zeta-values of arithmetic schemes at negative Integers and Weil-étale cohomology
    2018
    Co-Authors: Beshenov A.
    Abstract:

    This work is dedicated to interpreting in cohomological terms the special values of zeta functions of arithmetic schemes. Baptiste Morin and Matthias Flach gave a construction of Weil-étale cohomology using Bloch's cycle complexes and stated a precise conjecture for the special values of proper regular arithmetic schemes at any Integer Argument s=n. The goal of this thesis is to generalize their constructions to arbitrary arithmetic schemes (possibly singular or non-proper), while restricting to the case n We prove that the resulting conjecture is compatible with the decomposition of an arbitrary scheme into an open subscheme and its closed complement. We also show that this conjecture for an arithmetic scheme X at s=n is equivalent to the conjecture for A^r_X at s=n-r, for any r >= 0. It follows that, taking as an input the schemes for which the conjecture is known, it is possible to construct new schemes, possibly singular or non-proper, for which the conjecture holds as well. This is the main unconditional outcome of the machinery developed in this thesis

  • Zeta-values of arithmetic schemes at negative Integers and Weil-étale cohomology
    2018
    Co-Authors: Beshenov A.
    Abstract:

    This work is dedicated to interpreting in cohomological terms the special values of zeta functions of arithmetic schemes. Baptiste Morin and Matthias Flach gave a construction of Weil-étale cohomology using Bloch's cycle complexes and stated a precise conjecture for the special values of proper regular arithmetic schemes at any Integer Argument s=n. The goal of this thesis is to generalize their constructions to arbitrary arithmetic schemes (possibly singular or non-proper), while restricting to the case n We prove that the resulting conjecture is compatible with the decomposition of an arbitrary scheme into an open subscheme and its closed complement. We also show that this conjecture for an arithmetic scheme X at s=n is equivalent to the conjecture for A^r_X at s=n-r, for any r >= 0. It follows that, taking as an input the schemes for which the conjecture is known, it is possible to construct new schemes, possibly singular or non-proper, for which the conjecture holds as well. This is the main unconditional outcome of the machinery developed in this thesis. ALGANT DOC ProgramNumber theory, Algebra and Geometr

Milgram Michael - One of the best experts on this subject based on the ideXlab platform.

Peter Bertelsen - One of the best experts on this subject based on the ideXlab platform.

  • Compiling SML to Java Bytecode
    1998
    Co-Authors: Peter Bertelsen
    Abstract:

    instruction JVM instruction Jsconst ldc or ldc w Jaload aload !n?, aload, or wide aload Jastore astore !n?, astore, or wide astore Jdconst dconst !n? or ldc2 w Jdload dload !n?, dload, or wide dload Jdstore dstore !n?, dstore, or wide dstore Jfconst fconst !f?, ldc, or ldc w Jfload fload !n?, fload, or wide fload Jfstore fstore !n?, fstore, or wide fstore Jgoto goto or goto w Jiconst iconst !i?, bipush, sipush, ldc, or ldc w Jiinc iinc or wide iinc Jiload iload !n?, iload, or wide iload Jistore istore !n?, istore, or wide istore Jjsr jsr or jsr w Jlconst lconst !l? or ldc2 w Jlload lload !n?, lload, or wide lload Jlstore lstore !n?, lstore, or wide lstore Jnewarray newarray, anewarray, or multianewarray Jret ret or wide ret Jreturn areturn, dreturn, freturn, ireturn, lreturn, or return The bytecode emitter translates each of the above abstract bytecode instructions into the most compact of the corresponding JVM bytecode instructions. By introducing this level of abstraction over the instruction set of the JVM, the user of the SML-JVM toolkit is relieved from worrying about details in the JVM instruction set, e.g. which of the JVM instructions iconst !i?, bipush, sipush, and ldc should be used for pushing an Integer constant onto the operand stack. The user just inserts an abstract Jiconst instruction with an Int32.int Argument, and the bytecode emitter then chooses the most compact of the corresponding JVM instructions based on the value of the immediate Integer Argument. All other abstract bytecode instructions than those listed above are mapped directly to the corresponding JVM instructions. For example, the abstract instruction Jdup simply maps to the JVM instruction dup (represented in binary form as opcode 89). 3.4 Generating A Class File Generation of a physical..